Okay, yes, so we have plenty of ideas here. Now how to solder this thing. Yes, it actually is possible with your blunt tip soldering iron, purportedly you just need practice. Put the tip on the connection and the wire to heat them up, and the solder on the connection but don’t let it touch the tip. The heat will draw the solder in and fill up the area, so I am told. Be careful not to leave the soldering iron on there for more than 5 seconds, otherwise you could damage your components. Also, make sure you are careful with ventilation and not breathing in the fumes, and wash your hands after soldering. To remove solder, there are wicks you can use: put the wick on the area you want to remove solder, and heat the wick by putting the iron on top of it. The wick will fill up, so you can gently pull it across the board to sweep up more solder.
Use tape to help hold in place components with very short leads.
Fat soldering iron tip? Don’t worry. Use a magnifying glass, or, er, 10x stereo microscope, and with practice even the tiniest of joints can be soldered with such a fat iron.
20180312/DuckDuckGo raspberry pi how to solder very small connections
soldering iron radio shack
20180312/https://www.reddit.com/r/raspberry_pi/comments/59imi3/do_i_have_to_actually_solder_a_gpio_header_onto/
20180312/https://www.raspberrypi.org/forums/viewtopic.php?f=8&t=2025
20180312/http://mightyohm.com/files/soldercomic/FullSolderComic_EN.pdf
20180312/https://web.archive.org/web/20120510134519/http://www.solderinguide.com/
20180312/DuckDuckGo raspberry pi small tip tiny soldering iron
20180312/https://www.raspberrypi.org/blog/soldering-is-easy-comic/
Okay, so we also need some kind of board to practice soldering on too. Can we make our own? Probably, but the holes might not be as small as you want to practice on.