there is a lot of context you left out, what tires? what year is the bike? I converted a fuji nevada wheels to tubeless however it meant switching tires. Tires should be tubeless ready before going down this road. Tubeless tires have more rubber on the sidewalls to prevent sealant from weeping. non tubeless tires will weep for a bit which some people are fine with. Rims you have to do a ghetto conversion by using gorilla tape and run a couple of layers but also at the same time take a bit of work to get the bead to seat. tubeless ready rims are easier to seat. My current bike has tubeless ready rims and tires with proper rim tape and is much easier to get setup. Also unless you are facing constant punctures there really isn't a reason to go tubeless. Its possible to ride and do well without running tubeless.
tldr: yes you probably can but will be a bunch of work. I've done it but I would rather have tubeless ready tires and rims. unless you are getting constant punctures stick with tubes.