With the ‘standard’ DuPont headers that generally get used with Pi hardware (and a lot of other computer hardware for that matter), soldering is required both to provide a solid mechanical connection between the header and the board, and to establish an actual electrical connection between the pins and the pads.
You can, however, get press-fit headers instead, generally known as ‘hammer headers’ among the Pi community because of the branding of the ones offered by Pimoroni. You literally just line these up properly, and gently tap the top with a small hammer a couple of times to pop them in place. They have a couple of issues though, namely that they may not provide a reliable connection if there’s lots of movement or vibration, and that in some environments they may run into issues with corrosion. You also have to be careful when installing them to avoid bending the pins or the board (especially the board, you can straighten pins, but too much bend on the board in the wrong place and you’re popping out solder joints).
That said, soldering is a skill just like anything else, and with a little practice and patience, through-hole headers like this are a relatively easy soldering job.
If you actually have interest in learning to solder (it’s actually not very hard, and this is coming from someone who has terribly unsteady hands), you can generally find DIY electronics kits oriented towards teaching basic soldering skills many places online for less than USD 25 each, ranging from simple preprogrammed LED displays, to simple digital clocks or FM radios, to more complex stuff like LED tetris games. Speaking from experience, these are a great way to learn without shelling out lots of money.