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)
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)