As others have reccomended here, get a filter thing, or a cold brew maker. It doesn't make the brew better, but it makes cleanup so much easier. Which is good if you're making it regularly.
When I make cold brew I tend to use a filter bag, makes cleanup a lot easier. While I would love to go on a tangent about sourcing local specialty coffee & grinding just to your dose to keep your beans fresh, those don't matter quite as much for cold brew as they do for espresso & pour over. What really matters is if you enjoy the end result, so if there's anything that you don't particularly enjoy about your cold brew you can determine the root cause & adjust accordingly.
If you've got drip coffee filters, I would just pour the final brew through a drip coffee brewer and into another vessel (provided that you have a large enough brewer). It might take a bit longer than the steel filters, but the resulting cold brew is extremely clean tasting and you won't have to buy an additional thing to store.
Pretty much any cloth "cold brew bag" will do. There are metal tea infuser style ones that work as well, but personally I prefer the result from a cloth filter over metal
I use a stainless steel filter with a 100 micron mesh. It drops right into the mason jar for steeping. When it's ready, I pull out the filter, dump the grounds, rinse it out, and start the next batch. I've seen filters with more fine or course meshes, but I find the 100 micron to be good for course-ground coffee, like is typically recommended for a french press.
Personally I do not make concentrate. I use a smaller amount of grounds to make ready-to-drink cold brew. But you can do it either way.
Assuming you're using fresh beans, coffee releases c02 when exposed to water. It's usually the first step in pourover recipes and you can usually see it pretty dramatically.
The bloom for cold brew is just to prevent the gasses popping on your lid if you try to close it too early or overflowing. If you fill the jar with your coffee, then all the way to the top with your water, this blooming phase will spill over water and most likely the crust of all the coffee that hasn't saturated and sunk to the bottom yet. No good. The hour I have in my recipe is definitely overkill but it's just an easy (and lazy) easy unit of measurement to call out.