Yes, depending on the bank's policies, he can qualify for a loan, that is, there is no federal or state law of which I am aware that prohibits a bank from lending to an undocumented individual. A co-signer will surely help. He may also be eligible for private school or foundation scholarships. The credit union would be a good place to look first.
Through his DACA approval he would receive an employment authorization card which he can use to obtain a new Social Security card which won't read "Not Valid for Work". His number will be the same, but he can get a new card. Aside from that issue, I agree with my colleague - the requirements vary by bank or by loan, but it's possible that the actual requirement is that he be "lawfully present in the United States". What "lawfully present" means is actually somewhat complicated, but in some contexts, deferred action is included. I suggest obtaining his new Social Security card once he is approved for DACA, and if the problem persists, contacting an attorney at that time. I have attached a link you may find useful. Good luck!
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