Who said "life is suffering"?

The origin appears quite obvious. There is the word 'jati' in the scriptures, which means 'a class of beings', as follows:

[Due to ordaining as a monk] ‘Ever since I was born in the noble birth, sister, I don’t recall having intentionally taken the life of a living creature. By this truth, may both you and your baby be safe.’

‘yatohaṁ, bhagini, ariyāya jātiyā jāto, nābhijānāmi sañcicca pāṇaṁ jīvitā voropetā, tena saccena sotthi te hotu, sotthi gabbhassā’”ti.

MN 86

And what is birth?

Katamā ca, bhikkhave, jāti?

The birth, co-conception, emergence, production of beings in this & that class of beings; the manifestation of their aggregates, and [mental] acquisition of their sense objects.

Yā tesaṁ tesaṁ sattānaṁ tamhi tamhi sattanikāye jāti sañjāti okkanti abhinibbatti khandhānaṁ pātubhāvo āyatanānaṁ paṭilābho.

SN 12.2

'A being,' lord. 'A being,' it's said. To what extent is one said to be 'a being'? Any desire, passion, delight, or craving for form, Radha: when one is caught up there, tied up there, one is said to be 'a being.'

"Any desire, passion, delight, or craving for feeling... perception... fabrications...

"Any desire, passion, delight, or craving for consciousness, Radha: when one is caught up there, tied up there, one is said to be 'a being.'

SN 23.2

There was obviously a time in Buddhism, particular with the concoction of the Jataka Tales, the word 'jati' or 'jata' came to refer to a physical birth or a lifetime. This false view continues today, in false translations such as the following, where the word 'nivāsā' is falsely translated as 'lives' and the word 'jāti' is taken to mean a physical birth rather than a 'self-identity/class lineage':

When my mind had become immersed in samādhi like this—purified, bright, flawless, rid of corruptions, pliable, workable, steady, and imperturbable — I extended it toward recollection of past lives (nivāsā). I recollected many kinds of past lives. That is: one, two, three, four, five, ten, twenty, thirty, forty, fifty, a hundred, a thousand, a hundred thousand rebirths (jatiyo); many eons of the world contracting, many eons of the world expanding, many eons of the world contracting and expanding.

MN 4

When 'jati' is regarded as a 'lifetime' rather than as a 'self-view of a class of beings/self-identity' then verses, such as in the following dodgy translations, are misconstrued to mean life is suffering:

Now this is the noble truth of suffering.

Idaṁ kho pana, bhikkhave, dukkhaṁ ariyasaccaṁ—

Rebirth [life] is suffering; old age is suffering; illness is suffering; death is suffering; association with the disliked is suffering; separation from the liked is suffering; not getting what you wish for is suffering. In brief, the five grasping aggregates are suffering.

Jātipi dukkhā, jarāpi dukkhā, byādhipi dukkho, maraṇampi dukkhaṁ, appiyehi sampayogo dukkho, piyehi vippayogo dukkho, yampicchaṁ na labhati tampi dukkhaṁ—saṅkhittena pañcupādānakkhandhā dukkhā.

SN 56.11 First Sermon of the Buddha

Transmigrating through countless rebirths [lives],

Anekajātisaṁsāraṁ,

I’ve journeyed without reward,

sandhāvissaṁ anibbisaṁ;

searching for the house-builder;

Gahakāraṁ gavesanto,

painful is birth [life] again and again.

dukkhā jāti punappunaṁ.

Dhammapada

This false view & perversion of the Teachings becomes so obsessive that even Western monks today are now claiming the Pali word 'bhava' ('becoming') refers to a 'lifetime', despite compassionate efforts to dissuade them, such as found here: Bhava doesn’t mean ‘becoming’ by Sunyo Bhikkhu (a self-proclaimed Pali & Vinaya expert).

I would say it's the first noble truth. but to end it as stated would be wrong, and misrepresenting Buddha. The statement requires ellipsis(...) and would continue on as such...

1. Lifeforms suffer
2. to get what they want
3. they get (don’t get) what they want
4. this is the cycle. keep doing it, or make modifications (eightfold path + dhamma).

Regardless, to answer your question, the atomic idea "life is suffering" might have entered mainstream western thought through Arthur Schopenhauer's work.

“At all grades of its phenomenon, from lowest to the highest, the will disposes entirely with an ultimate aim and object. It always strives, because striving is its sole nature, to which no attained goal can put an end. Such striving is therefore incapable of final satisfaction.” Arthur Schopenhauer, The World as Will and Representation

Buddha NEVER said (translated into English, of course) "Life is suffering". He said that "there is suffering". It is important to clarify and highlight this significant difference.

The formulation, as you call it, is found in other philosophical systems of India dating back to 600-700 B.C. It is quite difficult to pinpoint which text "first" proposed it as such.