How soon can I use money from refi cash-out for a down payment?

[Dan Marl]

Hello everyone. 

A few months ago I bought a house cash. I was able to rent it out and just finished cashout refinance with an LTV of 75%. Can I use that money for a down payment for another house right away?

Will the new lender let me do that? Would they object to me using borrowed money for a down payment on the house I plan to get? Or do I have to wait for two months so that my last two bank statements do not show the deposit of the money I just borrow (from the cashout refinance)?

Thank you in advance!