Mocs should be pretty tight in my limited experience. Once they stretch, there is no way to make them tighter, and they can’t be cinched down to fit smaller feet.
The most common shoe measuring device is called a Brannock device, which gives you a length (i.e. US 8) and a width (i.e D, EE/Wide). I think width is US thing though, because I don’t see euro sizes with widths. Typically your sneaker sizes end up being bigger than your Brannock size, especially if you have a wide foot in Brannock size terms, because you can’t go wider than D with most sneakers, you end going longer to get enough width(going up .5 length gives roughly one more width size of extra width); another for that sneakers need to accommodate the thick end of socks. For example, my Brannock size is 6EEE, but most of my life I wore US 8.5D Nikes and US 8D Addidas. But US 7.5EE sneakers fit closer to my foot shape. My Oxford dress shoes are US 6.5EE; 6EEE also fit, but they look less sleek.
Back to climbing shoes, La Sportiva is very close to Brannock size in my opinion, I wear Euro 39 (US 6.5+D) in four La Sportiva models, with slight variations in fits. But Evolv Shamans are specifically designed to be closer to your street shoe sizes, so those in US 8 end up being the same fit. So 1-2 down from street sizes are not universal either. Your best bet is to try a couple sizes in your range to determine the best fit.
We haven’t started talking about high vs low volume feet yet.
I am sure your Mocs will stretch and/or your feet will get used to the smaller shoes. If you are just starting, a good fit is probably no dead space in front of your big toe and your toes are not curled.
Another anecdote: after taking a break from climbing for two years, I found that my old shoes were all way too tight when I first got back to it. I ended up getting a new pair half size bigger than my usual sizes. Six months of regular climbing later, all my old shoes are now comfortable, and my new shoes are too big.