Learn Russian: Мы работаем над своим стартапом с целью привлечь инвесторов. - We are working on our startup with the aim of attracting investors.

Both mean 'in order to,' but с целью (literally 'with the aim') is more formal and often used in business, academic, or professional contexts like talking about a startup. Using чтобы would also be grammatically correct but sounds more everyday and conversational.

Does с целью always take an infinitive like привлечь?

Yes, when expressing purpose this way, с целью is followed directly by an infinitive. Unlike для того, чтобы, you cannot use it with a past tense verb to introduce a new subject. It is used exclusively when the subject of the main clause is also the one performing the action in the infinitive.

Why is the noun phrase своим стартапом in the Instrumental case?

The phrase follows the preposition над. In Russian, to express 'working on' something, you use the construction работать над plus the Instrumental case.

Since the subject is Мы, could I use нашим instead of своим?

Yes, you could say над нашим стартапом, and it would be perfectly understood. However, Russian strongly prefers the reflexive possessive pronoun свой (in this case, своим) whenever the possessor is the active subject of the clause.