При условии, что оценщик уже здесь, оценка ущерба начнётся сегодня.

При условии, что means provided that, on condition that, or assuming that.

It is similar to если (if), but it sounds more formal and more explicit. It often appears in official, legal, business, or careful written language.

So:

• Если оценщик уже здесь, оценка ущерба начнётся сегодня. = If the assessor is already here, the damage assessment will begin today.
• При условии, что оценщик уже здесь, оценка ущерба начнётся сегодня. = Provided that the assessor is already here, the damage assessment will begin today.

The second version sounds more formal and slightly more conditional.

Because of the preposition при.

In this expression, при requires the prepositional case, so:

• условие → при условии

This is part of a fixed phrase:

• при условии, что ... = on the condition that ... / provided that ...

You do not usually change this phrase word by word; it is best learned as a set expression.

Because что introduces a subordinate clause.

In this sentence:

• При условии, что оценщик уже здесь = subordinate clause
• оценка ущерба начнётся сегодня = main clause

Russian normally separates subordinate clauses with commas, so the comma before что is required.

There is also a comma after здесь because the subordinate clause comes first and must be separated from the main clause.

So the structure is:

• subordinate clause, main clause

Because оценщик is the subject of the subordinate clause:

• оценщик уже здесь = the assessor is already here

The person who is here is the subject, so Russian uses the nominative:

• оценщик

If you try to analyze the clause by itself, it works like a simple sentence:

• Оценщик здесь. = The assessor is here.

That is why nominative is used.

Уже means already, and здесь means here.

So:

• оценщик уже здесь = the assessor is already here

The word уже adds the idea that this has happened by now, perhaps earlier than expected or by the relevant time.

Compare:

• Оценщик здесь. = The assessor is here.
• Оценщик уже здесь. = The assessor is already here.

Because ущерба is in the genitive case after оценка.

Russian often uses this pattern:

• noun + genitive noun

to express something like assessment of damage, repair of the car, reading of the book, and so on.

Here:

• оценка = assessment / appraisal
• ущерб = damage
• оценка ущерба = assessment of the damage / damage assessment

So ущерба is genitive singular of ущерб.

They are related, but they are different parts of speech and mean different things:

• оценщик = assessor / appraiser — a person
• оценка = assessment / appraisal / evaluation — the process or result

So in this sentence:

• оценщик is the person who does the work
• оценка ущерба is the assessment itself

This is a common Russian pattern: related words built from the same root but with different meanings.

Начнётся is the 3rd person singular future of the perfective verb начаться.

• начаться = to begin, to start
• начнётся = will begin

It agrees with оценка, which is singular feminine, but in the future form the ending here is just part of the conjugation pattern:

• оценка ... начнётся = the assessment ... will begin

Russian uses the perfective future here because it refers to a single completed starting point in the future: the assessment will start today.

Because the verb is начаться, not начать.

Compare:

• начать = to begin something, to start something
• начаться = to begin, to start

So:

• Они начнут оценку. = They will begin the assessment.
• Оценка начнётся. = The assessment will begin.

In your sentence, the assessment itself is the thing that begins, so начаться is the natural choice.

Russian word order is flexible, and placing сегодня at the end is completely natural.

The sentence first gives the condition, then the main event, then the time:

• При условии, что ... , оценка ущерба начнётся сегодня.

This sounds smooth and neutral.

You could also move сегодня for emphasis, for example:

• Сегодня оценка ущерба начнётся, при условии, что оценщик уже здесь.
• Оценка ущерба сегодня начнётся, при условии, что оценщик уже здесь.

But the original order is the most straightforward and natural in formal style.

It is fairly formal, mainly because of при условии, что and оценка ущерба.

It sounds like something you might hear or read in:

• insurance
• property damage reports
• business communication
• official planning
• legal or administrative contexts

In everyday speech, many speakers would choose something simpler, such as:

• Если оценщик уже здесь, оценку ущерба начнут сегодня.
• Если оценщик уже здесь, оценка ущерба начнётся сегодня.

So the grammar is normal, but the phrasing is somewhat formal.

Yes, in many situations здесь and тут both mean here.

So you could say:

• При условии, что оценщик уже тут, оценка ущерба начнётся сегодня.

But здесь is a little more neutral and often feels slightly better in formal or written language. Тут is very common in speech and can sound a bit more conversational.

So in this sentence, здесь fits the style better.

The correct pronunciation is with ё:

• начнётся

In many Russian texts, especially less careful or less educational ones, ё is often replaced in writing by е:

• начнется

But the meaning is the same, and native speakers understand both spellings. For a learner, it is helpful when ё is shown because it makes pronunciation clearer.

So:

• начнётся = more precise spelling
• начнется = very common in ordinary writing

Yes. Russian allows either order:

• При условии, что оценщик уже здесь, оценка ущерба начнётся сегодня.
• Оценка ущерба начнётся сегодня, при условии, что оценщик уже здесь.

Both are grammatical.

When the condition comes first, it sets the frame first: provided that ... When the main clause comes first, the sentence emphasizes the result first: the assessment will begin today ...

The original version is very natural because it introduces the condition before the outcome.