Avia meminit magnam messem olim sub sole calidissimo factam esse.

Because meminī, meminisse is a special verb. Its perfect forms are used with a present meaning.

So:

• meminit = he/she remembers
• meminerunt = they remember
• meminerat = he/she remembered or had remembered, depending on context

This is one of those verbs that English-speaking learners simply have to get used to. In form, meminit looks perfect; in meaning, it is usually present.

Latin often uses an indirect statement after verbs of thinking, saying, knowing, hearing, and also remembering.
That is what you have here:

• meminit = she remembers
• magnam messem ... factam esse = that a great harvest was made / had been gathered

In an indirect statement, Latin typically uses:

• an accusative subject
• an infinitive verb

So instead of an English-style that-clause, Latin prefers the accusative-and-infinitive construction.

Because in an indirect statement, the subject of the infinitive goes into the accusative case.

Here, messem is the subject of factam esse, not the direct object of meminit in the ordinary sense.

So the structure is:

• magnam messem = a great harvest
  but in the accusative because it is the subject of the infinitive
• factam esse = to have been made / to have been gathered

This is a very common Latin pattern and often feels strange at first to English speakers.

Because this is the perfect passive infinitive.

It is formed from:

• the perfect passive participle: factam
• plus esse

So:

• factam esse = to have been made
• more naturally in context, to have been gathered / brought in

Since the sentence is in indirect statement, Latin uses an infinitive instead of a finite verb like facta est.

Compare:

• direct statement: magna messis facta est = a great harvest was made
• indirect statement: ... magnam messem factam esse = ... that a great harvest was made

Factam agrees with messem.

Since messis is:

• feminine
• singular

the participle must also be:

• feminine
• singular

So:

• messem = accusative singular feminine
• factam = accusative singular feminine

And it is not factam est because the sentence is not using a normal finite verb here; it is using the infinitive construction factam esse.

Sole is ablative singular.

With sub, Latin can use either:

• ablative for position: under
• accusative for motion toward: to under / underneath

Here there is no movement. The harvest happened under the hottest sun, so Latin uses:

• sub sole calidissimo

If the idea were motion toward a place under something, then the accusative would be possible.

Because it agrees with sole.

• sole = ablative singular masculine
• calidissimo = ablative singular masculine

It is the superlative form of calidus, meaning hottest or very hot.

So sub sole calidissimo means something like:

• under the hottest sun
• or more naturally, under the blazing sun

Olim is an adverb meaning once, long ago, or in former times.

Its position is fairly flexible, because Latin word order is much freer than English word order. Here it sits inside the indirect statement, modifying the event:

• magnam messem olim ... factam esse
• that a great harvest was once / long ago gathered

Latin often places adverbs where they give the best rhythm or emphasis, not necessarily where English would put them.

Because Latin relies much more on endings than on word order to show grammatical relationships.

In English, word order usually tells us who is doing what. In Latin, case endings already do much of that work, so the writer has more freedom to arrange words for emphasis, clarity, or style.

In this sentence:

• Avia is the main subject
• meminit is the main verb
• magnam messem ... factam esse is the indirect statement

The prepositional phrase sub sole calidissimo and the adverb olim are inserted inside that clause. To an English speaker, that can feel scattered, but in Latin it is normal.

Literally, yes: factam esse means to have been made.

But Latin often uses facere in broader ways than English uses make. With messis it can refer to the harvest being carried out, completed, or brought in.

So although the literal wording is made, a more natural English translation in context may be:

• that a great harvest had been gathered
• that there had been a great harvest

This is a good reminder that a literal gloss and a natural translation are not always the same thing.