How do GPs typically fund the setup costs before closing?

Generally speaking, fund managers will work with their attorneys to defer costs until the fund does a first close. Then, the fund manager can use some of the management fees and sometimes the fund itself to pay for expenses.

With regards to fund formation attorneys, please read the following:

https://govclab.com/2023/05/26/vc-fund-formation-attorneys/

Please read this for more information on managing fund expenses:

https://govclab.com/2022/11/07/managing-fund-expenses-for-venture-capitalists/