In the novelization of "Spider-Man 2", he did have a professional designer make it for him; it was a favor from the Flying Dutchman, in return for humiliating Bonesaw.
But that's neither here nor there. He's not a costume designer in the comics, & yet, at 15 years old, on a shoestring budget, he made what is arguably the best superhero costume in comics history & we accepted it. To downgrade from that would be a bad move.
Although I will say this; long before the first film went into production, like back in the 90's, I kicked around ideas for a Spidey film. (What fan didn't?) One of them was that he would make himself an incredibly lame, ultra-cheesy costume. Something that he could put together with what a teenage boy w/no money could get ahold of. And then, once his brief showbiz career took off, his agent/manager would put forth some cash & provide him with a much better suit.
That would've been my justification.