Should I choose the earliest start date?

I accepted an offer a month ago. Before I was given the offer, they asked when I could start. I said the end of January 2023. My plan was to finish the rest of 2022 at my current firm, and then have the month in January to transition. I told my current firm right after I accepted the offer that I would be resigning, and I offered to stay the rest of the year until they found someone to fill my position. At first, they agreed, but then after all the partners spoke, they decided to have me leave later that week for liability/security reasons since I’m still working in the same industry.

The recruiter who connected me to the position reached out to me this week to see when I stopped working at my current job (I guess now my previous job). She said the team I’ll be working with in 2023 wanted to invite me to a party in January, but would only have me do so if I’m not working at my previous firm at the time of the party.

I explained why things ended earlier than I thought at my previous firm to the recruiter, and felt that I needed to offer to start sooner given how much transition time I’m having between the two roles.

HR reached out to me today and asked if I’d want to start the on January 9th or 17th. I want to say 17th, but I’m concerned it would make me look bad to not take the earlier option. Any thoughts? I’m not sure if I’m overthinking. My parents think I should take the earliest option they want me to start. I’m just scared I’ll look lazy for having had such a long transition. Thanks for any thoughts.