That’s exactly what happened to me. I was vaccinated and boosted and was with family at a baby shower on a Saturday. Got a text Monday night that a family member who was there had started having symptoms on Sunday and tested positive Monday. I had very mild symptoms on Monday but tested negative with a rapid test. Much worse symptoms on Tuesday but still negative on rapid test. Wednesday I had a PCR test and was positive. Was curious after I got the positive PCR so I took also took a rapid test Wednesday and that was positive. So, it seems it took me 4 days from being exposed and 2 of symptoms before I tested positive.
We were hoping to visit my daughter at school about 2 weeks later so I was trying REALLY hard to keep my husband from catching it so I basically lived upstairs in our house and he stayed on the main floor. After a week or so from testing positive I started doing rapid tests daily and it took a good 10 days after my first positive to test negative with a rapid test, which was probably about 2 weeks after I was exposed.