How do different denominations explain the apparent silence or hiddenness of God in our time?

Consider two classes of miracles.

Necessarily supernatural. Raising people from the dead and walking on water fall into the category of things requiring a special intervention by God, what we consider supernatural action that violates normal physical laws. These have always been exceedingly rare.

Rare events. Other miracles are rare events carried out by natural means that happen at a felicitous time, often predicted by a prophet, bringing rescue or judgement. Without detailed observations, many of this latter kind may be falsely assumed to be of the former.

Examples.

The area near where Sodom and Gomorrah once were has bitumen deposits. It has been hypothesized that an earthquake compressed the bitumen and shot it out as geysers which fell upon the towns and caught fire.

One scientist modeled the Red Sea and its particular undersea ridges and concluded that a steady wind of about fifty mph from the right direction would after 12-15 hours cause a separation of the waters permitting people to walk across.

As for the cattle plague upon Egypt, Rinderpest used to kill 90% of cattle and spreads fast.

Many (but not all) of the miracles in the Bible could be such felicitous events, technically natural but very rare. The only miracle was that the prophet was given advanced warning and this permitted the righteous to benefit or served as a warning and object lesson when the wicked suffered.

Now fast forward to the centuries since Christ rose from the dead. There are still prophets and healers in the church, but none create authoritative Scripture; the canon is closed. Thus the words of these prophets have more limited reach. This would seem to indicate that God has deprived modern people of the level of engagement that He formerly had with the people in Bible times.

How can we tell? What has changed is the separation in time between the prophecies and the miracles. Since the canon is closed, all major miracles (natural or supernatural) that happen in our day must have been announced by the ancient prophets, Jesus, or John who wrote the last book of the Bible, Revelation. We don't generally have a Moses telling us what is happening today or next week. The challenge is for us to study the Word and discover what those prophesies are so that we may grow our faith and find guidance. For that we have the Holy Spirit and the church to teach us.

The Biblical justification?

Surely the Sovereign Lord does nothing without revealing his plan to his servants the prophets. (Amos 3:7)

In order to determine one way or the other whether God is performing more or fewer miracles, we would need to lay out all the prophecies on a time grid to see whether any centuries are denser or sparser in coverage. The problem with this is that it is difficult to determine what is a prophecy and to when it applies. Also some prophecies have multiple applications throughout history.

In my personal research I have attempted this. I have found at least a dozen prophecies per century for all the centuries since Christ. I shall soon be publishing my results. I have found some centuries seem to be the subject of more prophecies than others, but my knowledge of history is uneven, so I can spot more propehecies in eras that I know in greater detail. Certainly the last two centuries are not among the sparse generations.

One extended prophecy concerns the plagues on Egypt. In addition to being a record of miracles that happened during the time of Moses, they also prophesied future judgements during the church age. Each plague (and a matching commandment) corresponds to a 240 year period of history starting with the birth of Christ. The sixth period of this prophetic clock thus ran from 1200-1440 AD. The sixth commandment against murder was broken by the church and Christian kingdoms due to their persecution and oppression of others. The punishment - matching the plague of boils from Exodus - was the Black Death or Bubonic Plague. Similar correspondences can be shown for each plague and commandment. Other prophetic clocks may be found in Ecclesiastes, Psalms, Job, and Matthew. Such clocks can contain scores of prophecies, all arranged in Chronological order, ensuring that no era in history is omitted. God was deliberate and detailed in His Word. There is no favoritism with him.

To prevent your question being closed down (for not being 'aimed' at a particular group within Christianity), I am going to answer as one who believes that God does, indeed, communicate in certain ways today, though such ways are largely different to the instances you refer to, in the distant past.

I can see how your main question is linked with your secondary, final question, though someone has suggested you remove that last question and post it separately. So, I will start at the beginning of your post, and see how far that can go.

First part of my answer: The Old Testament does have a great many examples of God miraculously intervening on behalf of his people, or of warning them when they continued to disobey, so that when his divine punishments came, they would know it was just as surely him acting, as when he acted to bless them.

However, even a cursory reading of the O.T. must take the huge time-line into account, and also the tiny size of the people of God who experienced his intermittent miracles. This reveals that there could be, say, 40 year's gap in miracles, or even hundreds of years' gap.

Take the generation that directly witnessed the ten plagues on Egypt so that God liberated them, then experienced the further miracles of the pillars of cloud and fire, the parting of the Red Sea with the destruction of the Egyptian army pursuing them. They also witnessed the awesome near-presence of God on Mount Sinai. A huge spate of miracles in a very short space of time! Ah, but shortly after, the people began to grumble against God, resented the food and water he miraculously provided, then disobeyed when the time came to enter the Promised Land. Only two out of ten spies urged them to go ahead; they heeded the eight. Therefore, God punished that whole generation by sending them back into the wilderness for 40 years, so that that generation would die off there, never getting into the Promised Land. (Read Numbers chapters 1:1-4 and 26:1-4 & 61-65.) Their descendants did.

Yet even in their punishment, that faithless generation experienced the miracle of their footwear and clothes never wearing out. Their children would no doubt remember that.

Second part of my answer: Fast-forward to God's punishment on his people, with the third deportation to Babylon in 586 B.C. The only people (captive in Babylon) who heard God speak, and witnessed miracles, were the likes of Daniel, Shadrach, Meshach and Abednego. Other prophets wrote what God told them, but from the end of the 'minor' prophets till the miracle of Jesus being born was around 400 years. There is a huge time-gap in scripture where the heavens were as brass.

Both parts put together: God rarely speaks or performs miracles. It is a mistake to read about such biblical events without noting the huge time gaps and how tiny the group of people were who witnessed them. Sometimes, only individuals did. But because the Holy Spirit caused written records to be made, copied, preserved and handed down through the centuries to God's people, we can read all about them. So, it might seem at first glance that God's voice and his miracles abounded when, in fact, even bouts of such divine activity were rare events, and many witnesses soon forgot and reverted back to unbelief, which always leads to ungodly living.

Conclusion: Don't assume that God does not appear to speak to his people outside of the Bible's accounts of miracles. You can only speak for yourself. You have no idea how many miracles and messages God conveyed to faithful believers throughout the centuries after the last book of the Bible had been written - and which he continues to do today, to those with ears to hear and eyes to see, that is.

After Jesus miraculously returned to heaven, the Holy Spirit was sent to indwell every believer, to teach, guide, encourage and assure. The Church Jesus started, which (he promised) the very gates of Hades would never overcome, continues to grow miraculously. Faithful preachers of the biblical gospel risk life, limb and everything to further the interests of the Kingdom of God, as they seek his righteousness (Mt. 6:33). Sometimes they experience a direct 'word' of direction, or a miraculous event. Sometimes not. The full number of the martyrs must be reached before God acts to bring vengeance on their killers (Rev. 6:9-11). And, throughout, God's people have his written word. But if they'd don't heed that, they need not expect a word, or an action, of favour to them, personally.

So, is your mind and heart open to the fullness of how God deals with his people? His arm is not shortened, that it cannot save; the Lord knows those who are his; not one person given to Jesus to be saved will be lost. The promises are still there. Do we believe them and act in faith? If so, then we will hear and see how God communicates with his faithful believers today.