Medical insurance after being laid off

I was laid off due to slow down. My effective termination data is Sep. 28. Then I got an offer later and the start data is October 15, but the HR in new company said my insurance will be effective after 30 days employment. I did not know this. I thought I will be covered on Day 1. So do I need to buy insurance now? Are there any negative impacts on the new insureace if there is a 6 weeks gap? Thanks.