According to Article III, Sec. 3, admitting a new state just requires Congress to approve—it doesn’t require Presidential approval. So Trump wouldn’t be able to stop it.
I think you might be mistaken. The sources I looked up all say that Congress must pass an enabling act, which has to be approved by the President, and the act of admission, like all other acts of Congress also has to be approved by the President. Congress does have the sole power to begin the process.