Stupid question time … the ESC’s pull a rather large amount of current. If you plan on soldering any of the leads that pull power/provide power, you need to consider the trace size and weight of the copper on your board or you will turn it into a fuse.
If you want to hook up the PWM signals that is fair game, but I would highly suggest staying away from any high current lead. On the PCB that you have posted, I would assume that the large pad areas are for the leads that you wish to solder to. As long as that board is actually designed for the job … then you can solder the leads directly to the board by tinning them and laying them length wise on the pad and flow solder.
Now on the soldering, if you don’t know how to solder I recommend someone who actually has experience so you don’t damage the board from excessive heat. The solder job is pretty sticking easy, but then again I have been doing it for over 50 years. If you are close to Southeastern Virginia, I could do that real quick for you.