When do I put in my 2 weeks notice after interviewing at another job?

So I work at Target and interviewed at a much closer Wal-Mart that promises better hours. The 1st interview was Sunday and went pretty well I think. The only thing I messed up on was when she asked to name a time I went above and beyond for a customer. I couldn't really think of anything lol.

Anyways, she told me to come back Thursday for a 2nd interview. Should I go ahead and put in my notice at my current job? If I do it now I can avoid being scheduled an extra week.

Or should I wait until Thursday to 100% confirm I have the job? I'll have to tell Walmart I have to wait longer to work if I wait. Do they care if it's like 2 or 3 weeks later after the interview?

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