You can, but you're limited to a single color since there's no way to register it, and if you're doing more than one item it's impossible to not smudge the print.
It makes it way easier to invest $12 and get some screenprinting clamps and attach them into a board of plywood or something.
Those blue presses are garbage. Don't waste your time and money trying to save a few bucks on a press. Crappy presses don't teach you anything but frustration. The learning curve for screen printing is steep enough without dealing with junk.
Look for a better used press on craigslist or Facebook Marketplace. If you want to buy new, look at a Hopkins press. If you're just going to start out with single colors, a set of hinge clamps is a great way.
Yes, they are junk. If you have been on this sub for a few years there have been numerous posts from users who thought they were getting a good deal on a press and regretted it.
Like u/Ballin_Hard420 says, save up a few more bucks and get a Hopkins, or look on craigslist or FB Marketplace for a good used press. The learning curve for screen printing is already steep enough without dealing with crappy equipment.
If you are only going to do one color prints, get a set of hinge clamps, they are much better than a junk press. Catspit YouTube channel has a great video on using a set.
If you're doing just one color prints this might be a economical option
https://www.amazon.com/Screen-ButterflyPrinting-Quality-Included/dp/B07FNTY64J
I started out with the speedball version of this but the squeegee looks much better on the Jacquard version. I quickly grew out of it and the below poster is right, you'll want a hinged setup (check out this tutorial for a DIY one. I built this exact one when first starting out. hinges can be purchased on Amazon.) Jacquard inks are nice and will work fine. a scoop emulsion coater was a god send when I first started out. if you're doing tees and are sick of the iron you can usually get a cheap heat press on amazon too without having to invest in a big drying unit. feel free to reach out with any questions. I'm still operating "garage boy style" but have been successful with my side hustle for about five and a half years now. good luck but more importantly, have fun and don't fear the mistakes!