Those kinds of SMT USB-C connectors are tricky if you aren’t using a stencil and solder paste.
My best suggestion would be to tin the pads with solder until there is a very slight pillow due to surface tension, use lots of paste flux, then put the connector down and use a heat gun to reflow it. You obviously can’t get a soldering iron on those pins as they’re almost captive.
Some of these kinds of vertical USB-C connectors have less stuff in the way of the pins. See:
However, having both rows being SMT on a USB-C connector is generally always tricky and terrible for hand work. What you probably want is something like this:
Note that has one row of SMT and one row of through hole. You can actually solder these with a soldering iron. The downside is that they almost always need a via of 0.65mm copper ring/0.40mm hole which some of the really cheap PCB services will bark at you for putting in your design.
I have tried a few times. I have failed each time.
I can do up to 0603-sized surface mount components but still can’t replace a USB C connector lol.
but if you’re up to the challenge, the electronics lab has the equipment to handle the job. I’ve successfully completed plenty of (less challenging) surface-mount soldering jobs at the space.