I quit a job after a week. The next week I was offered a new job which I accepted. I'm waiting for the background check to come back. I didn't put the job I had the week before on my resume. Will the background check find it? As far as they know I am collected unemployment.
It is highly unlikely that a background check will pick up or focus on such things as your one week of employment left off your resume. Depending on your geographic area, most effective background checks will work from several angles at once;
Through FBI or local or national law enforcement crime databases.
Through contacting companies "stated" on resume to verify employment dates.
Through references, social media and digital footprint.
So if you only worked there a week and there were no legal or criminal problems, it would not come up in the majority of background searches. Hope this helps. T