Do we ever use "suppose" (active) with infinitive?

What you have here is not what it first appears to be. There is an argument that "some people" criticise. These people recognise that it is unlikely that the Greek alphabet and the homeric epics took place at around the same time. [This, as you know, has to do with whether they were 'composed' and recorded in writing as single works by one author].

Blockquote

The use of the word 'suppose' in the context you have given, is suspect. I too have engaged in textual criticism of classical texts but as un undergraduate and later. The word 'suppose' is suspect. The argument is obvious:-

The proponents of this thesis try to <or suppose that they can> lessen this extreme unlikelihood by positing that the adapter was motivated by a desire to preserve in writing extraordinary versions of the the Homeric poems that he had heard performed.

The Cambridge English Dictionary online [https://dictionary.cambridge.org/dictionary/english/suppose] and its examples shows no example of the usage that puzzles you (suppose followed by to and the base verb lessen). I have not heard of one.

I can see no sensible explanation of how this mistake crept into the text. But the writer is saying that such an argument is what scholars call special pleading.

I am sure you also know that the argument does not give sufficient credit to the argument. The proper idea is of an oral tradition, which passed from generation to generation, which involved a complex mixture of improvisation, made easier by an armoury of stock names and phases: the sun invariably rose in exactly the same words ('early born rosy fingered dawn"), for example.

Greek writing, possibly picked up from Phoenicians, did not suddenly appear among Greeks of Asia Minor, and those who argue for a single author do notneed to make that claim. All we need is a literate literary genius to have heard those stories recited and composed version (or, like the brothers Grimm, compiled his (presumably not her) version.

Sadly, however, in relation to 'Suppose', in the words of the Roman poet, Horace, Homer nodded off.

No… We might just possibly get away with "Some people suppose 'to lessen the possibility' is to 'reduce the chance/(whatever)…" but that would assume "… suppose 'to…" didn't need to be "… suppose that 'to…"

That argument can be made without much difficulty but the fact of Asking shows that argument doesn't sit well with you.

It might be understood but basically nothing close to "Some people suppose to…" will be correct in ordinary English.