Миссия уже началась.

Уже means already.

So Миссия уже началась means that the start has already happened.

In Russian, уже often comes before the verb or the part of the sentence it emphasizes. Here it naturally modifies началась: the mission has already started.

Russian has no articles, so there is no separate word for the or a/an.

That means миссия can mean either the mission or a mission, depending on context. In this sentence, context tells us it means the mission.

Миссия is in the nominative singular.

It is the subject of the sentence — the thing that is beginning. In Russian, subjects are usually in the nominative case.

This is also the dictionary form of the noun:

• миссия = mission

Миссия is a feminine noun. Nouns ending in -ия are very often feminine in Russian.

Because it is feminine singular, the past-tense verb also appears in the feminine singular form:

• начался — masculine
• началась — feminine
• началось — neuter
• начались — plural

So with миссия, you get началась.

Russian past tense agrees with the subject in gender and number.

Since миссия is feminine singular, the verb must also be feminine singular past:

• Миссия началась.

Compare:

• Урок начался. — The lesson began.
• Лекция началась. — The lecture began.
• Собрание началось. — The meeting began.
• Переговоры начались. — The negotiations began.

The infinitive is начаться.

The ending -сь is just a variant of -ся used after a vowel. So:

• infinitive: начаться
• past feminine: началась

This verb is often called reflexive, but in sentences like this it is best understood as an intransitive verb meaning to begin / to start.

Compare:

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

So:

• Они начали миссию. — They began the mission.
• Миссия началась. — The mission began.

It can mean began, started, or has begun, depending on context.

Russian does not have a separate tense built like the English present perfect (has begun). Instead, Russian often uses the past tense where English uses either:

• simple past: began
• present perfect: has begun

Because the sentence has уже (already), the English translation has already begun or has already started sounds especially natural.

This is a question of aspect.

• начаться → perfective
• начинаться → imperfective

Началась is perfective, so it focuses on the fact that the start happened as a completed event. That is exactly what you want here: the mission is no longer just about to start — it has already crossed the starting point.

Начиналась would usually mean something more like:

• was beginning
• used to begin
• or it could set the background in a narrative

So in this sentence, началась is the normal and natural choice.

Yes. Russian word order is fairly flexible, but changing it changes the emphasis.

The most neutral order here is:

• Миссия уже началась.

Other possibilities:

• Уже началась миссия. — more emphasis on already, a bit more dramatic or literary
• Миссия началась уже. — possible only in a special context, usually with contrast; much less neutral

So learners should treat Миссия уже началась as the standard version.

The main stresses are:

• МИссия
• ужЕ
• началАсь

A rough English-style approximation is:

MEE-see-ya oo-ZHE na-cha-LAS'

A few notes:

• миссия has stress on the first syllable
• уже has stress on the second syllable
• началась has stress on the last syllable
• the final -сь is a soft consonant ending, not a full extra syllable

Yes, you might hear стартовать / стартовала, especially in contexts like launches, operations, projects, or events. But начаться / началась is the more basic and widely useful verb for to begin / to start.

So for a learner, Миссия уже началась is the safest and most general version.