Learn Russian: Команда работает день и ночь с целью запустить проект до зимы. - The team works day and night with the aim of launching the project before winter.

Yes, you could say для того, чтобы запустить or simply чтобы запустить. The phrase с целью followed by an infinitive is just a more formal, professional way to express purpose, often translated as "with the aim of" or "for the purpose of." It is very common in business contexts like this one.

Why is the perfective verb запустить used here instead of the imperfective запускать?

The perfective запустить focuses on the result: a single, successfully completed launch. If you used the imperfective запускать, it would imply the team's goal is merely the ongoing process of launching, or that they intend to launch projects repeatedly.

Why doesn't the phrase день и ночь have a preposition?

This is a fixed expression acting as an adverb, just like "day and night" in English. When expressing the duration of an action (how long something happens), Russian often uses the accusative case without a preposition. Both день and ночь are in the accusative case here to show continuous duration.

Both до and перед can mean "before." Why is до зимы used here instead of перед зимой?