The book "Avogadro Corp", which is otherwise not worth reading, has a plausible seeming mechanism for this. The AI, which can originally only send email, acquires resources simply by sending emails posing as other people (company presidents to developers requesting software to be written, to contractors for data centers to be built, etc.).

It probably wouldn't even be necessary for it to pose as other people, if it had access to financial assets, and the right databases to create a convincing fictional person to pose as.

If you seem human, it's not hard to get things done without ever meeting face to face.