Probably a variation of scouch (though Etymonline claims it modern and "imitative"). The verb sense "shift, scoot" is probably influenced by scoot.
Meanings
(US) To shift, move aside, or scoot over.
Turning over onto his back, he scooched down farther into his bag. It was the kind of sleeping bag with a hood built into it, so he pulled on the drawstring... 2002, Andrew Clements, A Week in the Woods:
"We could watch it all night," Joselle would add, scooching closer to her mother. "If it was on all night." 1992, Kevin Henkes, Words of Stone:
Lying on your side, start rocking back and forth, scooching to and fro and kicking. 1998, George Ostrom, Shannon Ostrom, Nature:
To crouch.
Thinks I to myself, “Sol, you're run off your course again. This is a rich man's summer ‘cottage’[…].” So I started to back away again into the bushes. But I hadn't backed more'n a couple of yards when I see something so amazing that I couldn't help scooching down behind the bayberries and looking at it. 1913, Joseph C[rosby] Lincoln, chapter I, in Mr. Pratt’s Patients, New York, N.Y.; London: D[aniel] Appleton and Company, →OCLC:
“Just a scooch?” she adds in a higher-pitched voice pinching her fingers together to highlight a small imaginary space on a spectrum […] 2018, Jessalynn Keller, Maureen E. Ryan, Emergent Feminisms: Complicating a Postfeminist Media Culture, Routledge, →ISBN:
Strolling to the stereo, Ronny turned the volume dial a scooch to the left, looking at the chef with what Jimmy's father would've called a smack-me face. “Hurry it up.” Chef Alfred was tasting the stock. He rapped the spoon against the ... 2018, Lillian Li, Number One Chinese Restaurant: A Novel, Henry Holt and Company, →ISBN, page 80:
Clan of the Papaya Whip Stymphalian Bird (just a scooch too long and would probably be better fit for a dessert at Bennigans), Pitchfork Shoebox Clan (maybe if you were a […]) 2008, Douglas Sarine, Kent Nichols, Ask a Ninja Presents The Ninja Handbook: This Book Looks Forward to Killing You Soon, Crown Archetype, →ISBN: