How could SAM give Alec Biotic powers?

I didn't have the heart to tell Cora. Sorry I know you should be Pathfinder now. But you see my dad put a little bit of space magic in my head. It makes me easily better then you, in something you have trained your whole life to do. It makes me better, stronger, smarter, and a better biotic then you. I could dance around your precious Sarrissa in my biotic glory and all she would be able to do is watch in awe. So you see, that is why I am Pathfinder and you are my lap dog. Have a nice day.

But I suppose that would have been a renegade interrupt, and they were removed.

Red sand can give non biotic users brief telekinetic biotic abilities.

Maybe Alec experimented with lacing the SAM implant with eezo? Or had it artificially imbedded into his nervous system?

He seems the type.

ME2 and ME3 both established that biotics can be engineered - Miranda was engineered as a biotic by her father despite being older than the earliest known human biotics by a good five years. ME3 established that asari biotics were the result of genetic engineering on the part of the protheans.

Did you make a barrier the size of a small ship?

I don't think so.

I've been playing Stellaris a bit (the game got an expansion) and the time and effort they put into intelligent deep scifi world building is great. Compared to 'We have to explain it? SAM of course. SAM, SAM!' it's even better.