Starting new website before old one expires

Maybe this is a really stupid question, but bare with me please..

I just canceled my domain with my hosting provider. They say my domain will still be available until 28/02 (when it expires).

Can I already start a new website on a different hosting provider, with different domain name and the same content of the old site?

It's a local business, so the site will probably look similar. I don't know if this will have a negative effect for SEO (duplicate content) since the old site still exists in Google.

Thanks for your advice

Yes you can go ahead and start building out your new site on the new host with the new domain.

Any reason you don't want to keep the old domain if it is already ranked?

So there won't be any duplicate content if I use a lot of the same text like on my first site???
I mean, it's just indexed already by Google. It's not that well ranked.

Is there any reason why you don't want to use the same existing domain? You can still use that domain with your new hosting provider in case you weren't aware.

I am not expert but from what I read, you need first deindex your old domain completely, this is either from Google webmaster tool or wait till natural drop of you domain on Google search (but with a very long time), at that time, you can reuse your contents on your new domain.

Yeah, I can deindex my old website first, and then start creating a new one I guess.
The first (old) domain looks really horrible, isn't ranked that good, basically I have to use "site:" to find it on first page (and this for a local site)

For me, I just want to start over fresh Also the domain name is better for SEO right now, and I don't want to mess with redirects.