Jest już blisko siódmej, więc muszę wyjść.

Because Polish usually tells the time with an ordinal number, not a basic counting number, when you say at/about a certain hour.

So:

• siódma = seventh
• implied noun: godzina = hour
• siódma really means the seventh hour, i.e. seven o’clock

In this sentence, the form is siódmej because of the grammar required after blisko. The full underlying idea is:

• blisko siódmej godziny = close to the seventh hour

In everyday speech, godziny is usually left out.

It is in the genitive case.

The word blisko normally takes the genitive, so the time expression after it must change form:

• nominative: siódma
• genitive: siódmej

Since godzina is feminine, the ordinal agrees with it:

• siódma godzina
• blisko siódmej (godziny)

So siódmej is not random—it is the feminine genitive singular form of siódmy.

That is simply how blisko works in this meaning. When it means near / close to / almost, it is followed by the genitive.

Examples:

• blisko domu = near the house
• blisko końca = near the end
• blisko siódmej = close to seven o’clock

So for a learner, the safest rule is:

• blisko + genitive

Już often means already, but in time-related sentences it can also feel like by now, as it is, or getting to be.

So Jest już blisko siódmej suggests something like:

• It’s already close to seven
• It’s getting close to seven now
• By now it’s nearly seven

It adds a sense that the time has advanced more than expected or enough for the speaker to react.

Polish commonly uses jest by itself in expressions about time:

• Jest pierwsza. = It’s one o’clock.
• Jest późno. = It’s late.
• Jest blisko siódmej. = It’s close to seven.

This is a normal impersonal way to state the time. English needs it, but Polish does not.

You could say To jest... in some contexts, but for telling time it would sound unnatural or overly emphatic.

Because Polish usually leaves it out when the meaning is obvious.

So instead of saying:

• blisko siódmej godziny

people normally say:

• blisko siódmej

The noun godzina is understood automatically. This is very common in time expressions.

This is mainly about aspect.

• wyjść = perfective, a single completed action: to go out / leave
• wychodzić = imperfective, ongoing, repeated, or habitual: to be going out / to go out regularly

In muszę wyjść, the speaker means a specific departure that needs to happen now:

• I have to leave

That is why the perfective verb wyjść fits well.

If you said muszę wychodzić, it could sound more like:

• I have to be leaving
• I have to leave repeatedly / as a habit
  depending on context

In everyday speech, both can appear in some situations, but muszę wyjść is the most straightforward choice for a single act of leaving.

Więc means so / therefore. It introduces a result or conclusion.

Here:

• Jest już blisko siódmej, więc muszę wyjść.
• It’s already close to seven, so I have to leave.

This is different from bo, which means because and gives a reason.

Compare:

• Muszę wyjść, bo jest już blisko siódmej.
  = I have to leave because it’s already close to seven.

The meaning is very similar overall, but the sentence structure and emphasis are slightly different:

• więc = consequence
• bo = cause

Because in Polish the verb form already tells you the subject.

• muszę = I must / I have to

So ja is usually unnecessary. Polish often drops subject pronouns unless they are needed for emphasis, contrast, or clarity.

Compare:

• Muszę wyjść. = I have to leave.
• Ja muszę wyjść. = I have to leave.
  This sounds more emphatic.

Yes, and that is a very common alternative, but the structure is different.

• Jest blisko siódmej = It’s close to seven
• Jest prawie siódma = It’s almost seven

In prawie siódma, the time expression is not after blisko, so you do not get the genitive form siódmej. Instead, you use the basic time form:

• siódma

Both are natural. Prawie siódma may sound a little more direct for almost seven, while blisko siódmej emphasizes nearness to that hour.

The given word order is natural, but Polish word order is fairly flexible.

Original:

• Jest już blisko siódmej, więc muszę wyjść.

Possible alternatives:

• Muszę wyjść, bo jest już blisko siódmej.
• Już jest blisko siódmej, więc muszę wyjść.
• Więc muszę wyjść — jest już blisko siódmej.

The basic meaning stays similar, but emphasis changes:

• earlier już can highlight the lateness
• putting muszę wyjść first can stress the action
• using bo instead of więc changes the logical presentation from result to reason

So the original sentence is normal and idiomatic, but not the only possible wording.