Job offer contingent on background check

Hi all-

I recently was offered a job I am very excited about. I have officially got the written offer, of course contingent on passing a background check. Should I give me 2-week notice to my current job? I have read a lot people say to not do this, but I know my background is clean. I recently underwent another background check with no issues. My credit isn’t great but I am in CA so they can’t run credit checks for jobs (only under certain circumstances can they run background checks but not for the position in question). Thanks!

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