Offer deferred, don't know what to do

My offer (from a FAANG company) has been deferred to January 2024. I don't know what to do now:

1. I have another job offer (~8 LPA), but that job requires me to serve notice period of 2-3 months

2. A startup's founder rejected me, saying he wanted someone for long term (he thought I'll leave next January)

Should I try for full time jobs? Many companies become unwilling to take me in, presuming that I will leave in January 2024.

Or should I look for internships (even though I have graduated)? Getting an internship won't help mitigate the risk of not having a fulltime job offer after graduation though.