Accepted job offer tentative of drug test should I give my notice?

I have a shitty full time at a hospital and I finally got a job offer! I received an offer from Walgreens to be a pharmacy technician and today they sent me a written offer letter. It had my start date, orientation date, pay rate, and I had to electronically sign and fill out a few forms. At the end of the email it says I will receive information to do a drug screen within 48 hours of accepting my offer.

My start date on the offer letter is 2 weeks from Monday and I want to give my notice tomorrow. Is that okay to do? I’ve never done drugs before and I had to take a drug screen recently for work anyway so I should be good right?

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