Transferring a Website to Squarespace - Downtime on existing host during transfer period?

I have an existing, active domain on a different hosting platform that I would like to transfer to a new website I have built on Squarespace. I have been reading about the transition period which the Help page suggests might take 15 or so days to complete.

I am wondering if there will be any interruption to my existing domain/website during this transition period-- i.e. Will my existing website be down during this transition period? I would assume not as that would make any transition very difficult because company's (including ourselves) cannot afford such downtime for their website.

I am assuming the answer to this is no but wanted to confirm before I initiate the transfer. Any insight from someone who has transferred an active domain to Squarespace would be helpful!

Thanks,Matthew