It's very clear from the context what he means using the idiom the shit out of it to mean to an excessive degree.
However, science is a noun but in this case is being used as a verb.
The bigger "idiomatic" point here--from which some amount of humor is drawn--is specifically vagueness. Invoking science in this way which is so abstract is to deliberately make it sound like he has no idea what he's talking about.
If you ask an educated person for help with something and if they would know the answer, and they said: "Sure I can help, I spent four years at collej." it has some of the same ring. It's not necessarily that they don't know the answer--but sounding deliberately ignorant "makes it funny".
However, other nonverbs don't seem to work
Bird the shit out of this.
In the right context, it could work just as well.
Imagine you were watching a bizarre cartoon (like Rick and Morty--which someone mentioned in a comment yesterday somewhere) there is a character named "BirdPerson". The following dialogue could easily happen in some episode with that character:
(Giant earthworms land and are wreaking havoc on a town)
Morty: "The worms are killing everyone! What are we going to do!"
Rick: "Gimme that phone..."
(Rick dials a number, Birdperson answers)
Birdperson: "What is it you require of Birdperson, Rick"
Rick: "Hey Birdperson. There's like...a lot of worms here. And
I figure that's your deal, right? So we need you to come
out here and like--uh--bird the shit out of them for us. Okay?"
Again this plays off the vagueness. If someone is half-bird and half-person, and you're fighting giant alien earthworms--you don't actually know what they would do to fix the problem. (Is Birdperson going to kill them? Eat them? Shoot them with lasers? Rick doesn't know, neither does the audience, so it's funny for him to fumble and just suggest that he "bird" them. It's meaningless, and the meaninglessness is why it's funny.)
Some other non verbs that seem to work
Orange the shit of it - (colour something orange)
While discussing what works and what doesn't--as written that doesn't "work". One might say "I'm going orange the shit into this thing". Again likely drawing humor from the vagueness.
- "I'm going to do something very intense, and very serious, I just don't know exactly how to phrase it yet because I haven't got an actual plan."