Yes.
You don't need a domain to run a website, you just need the web server set up and listening for visitors.
Now, when you say "launch", that is a marketing thing. If you want people to easily access your site on a certain advertised date, then the shorter and more memorable the better. Unfortunately, that can become more expensive the closer to that goal you get.
For free solutions, look into:
free subdomains (freedns.afraid.org is a good start)
free domains (.tk, .cc, etc)
create a subdomain on your current domain
give out the IP address (not recommended)
Answer from zoltar on Stack ExchangeThere is a way to get a free domain really for free? And that dont have any thing in the web when accessed?
I try noip, but, if i put "enable mask url" then noip put a horrible frame at the end of the webpage. I dont want that.
So, there is a way to get one? i dont matter if the url is afjhdalsfjhdslajkf.fdsafjañ.tk
or whatever.
dns - Can I launch my website without purchasing the domain name? - Webmasters Stack Exchange
Can I register a domain name without hosting the site?
Is there a way to register a free domain name?
a domain name for free? (really free...)
Can I easily transfer my domain name to another hosting provider?
Can I register a domain name without creating a website right away?
How can I protect my domain name against cybersquatting?
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Yes.
You don't need a domain to run a website, you just need the web server set up and listening for visitors.
Now, when you say "launch", that is a marketing thing. If you want people to easily access your site on a certain advertised date, then the shorter and more memorable the better. Unfortunately, that can become more expensive the closer to that goal you get.
For free solutions, look into:
free subdomains (freedns.afraid.org is a good start)
free domains (.tk, .cc, etc)
create a subdomain on your current domain
give out the IP address (not recommended)
Yes, sure you can do it. The domain name you purchase is/has to be registered on domain name servers which are basically key-value pairs linking your domain name to your server's IP address.
What options do we have..
You can access your site simply using your IP address. Make sure it's a public one.
If you own even a single domain for example, mydomain.com, you can create a subdomain for mydomain.com and that's free. In DNS entries you have to register subdomain.yourdomain.com points to your public IP and you are done.
As @Zekar said, you can go for the "free subdomains" and "free domains".