Can a non-Buddhist get Nirvana?

Can a Hindu or a Christian or a Muslim, who is not aware of Buddhist philosophy, get Nirvana?

No. If they accidentally got to Nirvana, they would be a Buddha themselves. In summary, the teachings of the above three religions cannot reach Nirvana.

Otherwise, why doesn't everyone become a Buddhist to attain supreme bliss

Because not everyone wants to abandon self, completely, 100%. Most Buddhists cannot even reach Nirvana so how do you expect the non-Buddhists to do so? The Buddha did not teach his dhamma was for all people.

And, Master Gotama, when having directly known it, you teach the Dhamma to your disciples for the purification of beings, for the overcoming of sorrow & lamentation, for the disappearance of pain & distress, for the attainment of the right method & for the realization of Nibbana, will all the world be led [to release], or a half of it, or a third?"

When this was said, the Blessed One was silent.

AN 10.95

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Then, having understood Brahma's invitation, out of compassion for beings, I surveyed the world with the eye of an Awakened One. As I did so, I saw beings with little dust in their eyes and those with much, those with keen faculties and those with dull, those with good attributes and those with bad, those easy to teach and those hard, some of them seeing disgrace & danger in the other world. MN 26

I have practiced Theravadin mindfulness meditation for more than 50 years. My meditation teacher, a Theravadin Buddhist monk, The Venerable Ananda Bodhi, formally told me that attained Enlightenment in 1979. I can say that Enlightenment is a psychological state of mind and that the belief is God would not prevent such Enlightenment. If you want to know more details, you can read one of my books available on line. My name is Ronald Cowen. I also have a Buddhist name, Sila Ananda, given to me during my novice ordination thirty years ago.

It is indeed possible to become enlightened (i.e. attain Nibbana) without becoming a Buddhist and without encountering the teachings of a Sammasambuddha. Such beings are called Pacceka Buddha or Pratyeka Buddha (see here and here), which literally means "private Buddha" or "lone Buddha". You can find some details in this question.

It is also true that Buddhism is very far away from (almost) every other religion, because of Anatta (no eternal self), and also the middle way between eternalism and annihilationism (see this answer).

In MN2, the Buddha stated clearly that having the wrong view of an eternal, independent and standalone self is not conducive to attaining Nibbana (permanent happiness and freedom from suffering). If one believes in an Eternal God, then this implies a belief in an eternal self who is the Eternal God, and therefore is also a wrong view, from the Buddhist perspective.

Not everyone becomes a Buddhist, partly because the full depth of the teachings may not be easy for all to understand as the Buddha stated in MN26:

'This Dhamma that I have attained is deep, hard to see, hard to realize, peaceful, refined, beyond the scope of conjecture, subtle, to-be-experienced by the wise. But this generation delights in attachment, is excited by attachment, enjoys attachment. For a generation delighting in attachment, excited by attachment, enjoying attachment, this/that conditionality & dependent co-arising are hard to see. This state, too, is hard to see: the resolution of all fabrications, the relinquishment of all acquisitions, the ending of craving; dispassion; cessation; Unbinding.

To be honest, even for Buddhists, Anatta and dependent origination may be hard to fully understand and realize through their own experience and discernment. For this is needed (along with other things), to attain stream entry.

However, according to Buddhism, every person, regardless Buddhist or non-Buddhist, have the right to impermanent forms of happiness, including the right to be reborn in the heavans.

Christians who practise John 13:34-35 and Hindus who practise BG12.13-14, would be fulfilling the Buddhist practice of the Brahmaviharas (at least one or two of them), which should lead them to heavan (but that would not be permanent).

I once asked a similar question here, where you can find some quotes showing that the description of Nibbana sounds similar to the description of Tao and Brahman/Atma. So, you can also draw some relief from there that there is some degree of overlap, but nevertheless, Anatta is a core part of the teachings and cannot be compromised.

It depends more on what each teacher teaches & less on what the religion of the teacher is.

It depends more on the students ability to teach themselves the important details that even the best teachers cannot teach.

According to the Tipitaka, if a non-Buddhist teacher teaches something similar to the Eightfold Path then the better the chance that the teacher's students will become arahants.

Absolutely – nirvana is religion-agnostic. It doesn't matter what religion you consider yourself to belong to as these are essentially just labels anyway; what's important is what you practice.

"Can a Hindu or a Christian or a Muslim, who is not aware of Buddhist philosophy, get Nirvana?"

Yes.

"If yes, how?"

With insight gained from meditation.

"Otherwise, why doesn't everyone become a Buddhist to attain supreme bliss?"

You don't need to become/be a Buddhist to attain supreme bliss.

Nirvana is often thought of as a Buddist exclusive thought but Dictionary.com difines Nirvana as a Hindu concept also and adds "a place or state characterized by freedom from or oblivion to pain, worry" which could well be applied to the Christian concept of heaven.

No religion teaches what Buddhism teaches at its core.

If the teachings of the religion are complete, they would be the same as the teaching of another complete religion. By "complete" I mean universally acceptable. If the teachings of a religion cause conflict in an individual, the teachings are clearly not complete.

So, assuming what's being taught in Buddhism lets the individual live a conflict free life (or enlightenment), then any religion's teaching that let the individuals live a conflict free life is ok to be followed.

A true Hindu or Christian or Muslim believes in God and soul.

First thing - what you believe in, doesn't matter. What really is true - does matter. You may believe that Earth is flat but it doesn't matter. What matters is that Earth is spheroidal and just because you don't believe in it, doesn't change it.

Believing or not believing in God and Soul is immaterial. What is of importance is to know whether God and Soul really do exist. And if they do, then what are they?

Water is called with different names in different cultures. But all those names actually point to the same liquid with unique attributes. If God and Soul are real, then every complete religion would acknowledge them. And if the religion does not acknowledge them, and given that they are real, the religion cannot lead you to a conflict free life because the teachings of the religion are in conflict - the religion is saying that God and Soul do not exist when they actually do.

Can a Hindu or a Christian or a Muslim, who is not aware of Buddhist philosophy, get Nirvana? If yes, how?

Nirvana is a state. It is not tied to any religion. It is a real state (of an individual) and therefore in complete religions it should have an acknowledgement.

This state, which is called Nirvana in Buddhism, may be called with other names in other religions but the Nirvana of Buddhism would be same as Nirvana of Hinduism, Christianity or Islam, even if it is called with different names in those religions.

The relation that a Hindu mother feels with her child is the same as a Christian mother feels with hers is the same as a Muslim mother feels with hers. The relation is called by different names but the feeling is exactly the same.

Otherwise, why doesn't everyone become a Buddhist to attain supreme bliss?

Because it doesn't matter what path you take. What matters is that you attain enlightenment.

why doesn't everyone become a Buddhist to attain supreme bliss?

I think that a "true" Christian may have beliefs which (may) help them to find some peace or solace, and which have some similarities at least in their effect (if not in their form) to Buddhist beliefs. I guess for example, faith that "It's God's will" or "This is part of God's plan", and the "Lord's Prayer" that, "Let thy will (not my will) be done", might help to alleviate a personal craving for something to be other than it is (and therefore, alleviate that type of dukkha). Similarly the virtue of Charity (which is Christianity's "greatest" virtue, and the second of the two "great commandments") remind me of some things which the Dalai Lama has written, about caring for other people to avoid being trapped in your own "self".

I know less about Hinduism; but a while ago I asked about this story which I half remembered, Self like a diamond, because I assumed its moral was Buddhist: I recently discovered that story is from a Shivaite tradition ... which I haven't been taught, but of which I get the impression that the principal doctrine, attitude, or action seems to be something like, "Everything is God, let me lose my self in order to find or be with God" ... so again there's some kind of non-self doctrine happening there.

I'm not trying to say that these other traditions are as good as Buddhism, nor the same as Buddhism ... but perhaps they address or attempt to address some of the same human frailties ... and people's needs are at least partly addressed by the religion they have.

Another answer to your question is that there are historical reasons. The Buddhadharma has existed in the West for only about the last 100 years or so ... if you learned any religion from your parents, it probably wasn't Buddhism.

Sometimes people who have any existing religion might be averse to learning or practicing a new one: Islam may penalize apostates; Judaism (and Christianity) have the first commandment; see also Meditating and including buddhist philosophy in your life without abandoning previous religious beliefs?

Then again, maybe your premise ("why doesn't everyone become a Buddhist") is wrong ... maybe everyone does become Buddhist! I discovered that "zen" has become a well-known, everyday or "current" adjective in France ... a synonym for cool or calm, detached, unstressed. So everyone has some idea of what it means, what its values are. People who are interested can find more ... there are many centres (e.g. in Paris), there's Plum Village, there are books in a large local book store, etc.

Also, as I said in How to explain what Buddhism is?, I've found that not everyone seems to feel the need for what Buddhism has to offer ... and/or that Buddhism isn't sufficiently well taught, well explained to people ... so that's another reason that not everyone is interested. I won't say "there aren't enough good Buddhist role models for people emulate" because maybe that's not true, however maybe those good role models (who other people might meet every day in society) aren't people who preach, or teach that Buddhism is essential -- How are Buddhists supposed to spread Buddhism?

Finally the answer I accepted to that question suggests that there are different forms of Buddhism ("each branch has a slightly different take on what the problem is that Buddhism is meant to solve"). If you think there's "one true form" of Buddhism which results in "getting Nirvana", you might note that not even all "Buddhists" will become that type of Buddhist.

Attaining Nirvana is not about labeling one self as Buddhist. To attain Nirvana you should follow the path to Nirvana. Any body following this path will reach the destination regardless of what they call themselfs. So you can call yourself a Buddhist, Hindu, Christian, Muslim, Jain, Jew, etc. to start with but what matters to realise Nirvana is the threefold practice.

As the realities unfold through direct insight your faith in Buddhism concepts also will get stronger at level of experiential verification, i.e., you have see in reality that the theory is inline with reality. Likewise at some point you will see there is nothing worth identifying as self or nothing that you completely can control. This is the Buddhist concept of non/not self.

Can a non-Buddhist get Nirvana?

Buddhism, Hinduism, Islam etc. are just words, conventional language. What is important is the teaching and practice of the teaching.

In the famous Maha-parinibbana Sutta, there is a passage where the Buddha explains to the wandering ascetic Subhadda, that "in any doctrine & discipline", that does not contain the Noble Eightfold Path, enlightened beings cannot be found.

It shows that only teachings that contain the Noble Eightfold Path can lead to freedom from suffering, to Nibbana.

The quoted passage can be found below.

Then Subhadda went to the Blessed One and exchanged courteous greetings with him. After an exchange of friendly greetings & courtesies, he sat to one side. As he was sitting there, he said to the Blessed One, "Venerable sir, these brahmans & contemplatives, each with his group, each with his community, each the teacher of his group, an honored leader, well-regarded by people at large — i.e., Purana Kassapa, Makkhali Gosala, Ajita Kesakambalin, Pakudha Kaccayana, Sañjaya Belatthaputta, & the Nigantha Nataputta: Do they all have direct knowledge as they themselves claim, or do they all not have direct knowledge, or do some of them have direct knowledge and some of them not?"

"Enough, Subhadda. Put this question aside. I will teach you the Dhamma. Listen, and pay close attention. I will speak."

"Yes, lord," Subhadda answered, and the Blessed One said, "In any doctrine & discipline where the noble eightfold path is not found, no contemplative of the first... second... third... fourth order [stream-winner, once-returner, non-returner, or arahant] is found. But in any doctrine & discipline where the noble eightfold path is found, contemplatives of the first... second... third... fourth order are found. The noble eightfold path is found in this doctrine & discipline, and right here there are contemplatives of the first... second... third... fourth order. Other teachings are empty of knowledgeable contemplatives. And if the monks dwell rightly, this world will not be empty of arahants."