Sid ranks pretty low on the list of possible fathers, but only because he's married to Hannah. They're currently in a long-distance relationship.
Still, Hannah seems to be spread pretty thin with work. Who can forget when she had to cut her own engagement party short in the pilot episode to fly back to Los Angeles to perform a transplant surgery? She and Sid also got into a major fight about how he bought his bar without telling her, and those issues could continue to bubble up. While Sid and Hannah are happy now, the whole long-distance thing could throw a wrench in their romance down the line.
Sid and Sophie probably interact the least out of the main cast, but some fans are convinced that's just to keep them off the scent. But his presence in the Valentine's Day episode also seems to indicate it's not him.
Yet, he's certainly not the least probable.