Russian uses the past tense form for unreal conditionals and similar clauses with бы (the conjunction чтобы is essentially что combineed with бы).
When using чтобы, the form depends on whether the sentence concerns two entities of just one.
If someone wants someone else to do something, the past from is used:
- Мы попросили, чтобы они пришли завтра. = We asked that they come tomorrow
If it is the same entitity who does something in order to achieve something, the infinitive is used:
- Я пришёл рано утром, чтобы всё успеть. = I came early in the morning to have enough time to do everything.