I finally soldered the chip on my own without a reflow oven. It was way easier than I was expecting, thanks to many comments and some videos found on YouTube.
- Soldering iron, 2mm head
- Solder wire with incorporated flux
- Flux in a syringe
I first tinned the top-left pin footprint in order to be able to place the chip for further solder. I then melted the tin again and placed the chip with a little clamp with accuracy to make sure that all the pins were on the corresponding pin footprint. I then soldered the opposite pin. After that, I was sure that the chip would not move during the rest of the process.
I started to solder each pin one by one until two pins got linked due to my lack of soldering skill. To correct my mistake, I put a drop of flux on and then I heated both pins with the soldering iron. With much surprise, it appears that it perfectly corrected the mistake. For the other side, I linked half the pins together on purpose and then use some flux. It's way easier, faster, and produced a cleaner soldering result.
Here is the result of the process:
I did some research about the oven part of the post. It appears that it's possible to use an unmonitored heat control oven (like a kitchen oven) to solder an entire board at once. Since it's non-monitored, it is not advisable to solder sensitive chips. However, it's pretty safe to solder every resistor and capacitor with the oven and then solder chips like this with a soldering iron. (Now I know how to do it properly so it's no big deal.)
But please, DO NOT use the oven you are using to bake food!
Solder wire/paste releases toxic fumes when it melts, so use a dedicated oven that you are sure to not use again.
I made this answer with the help of comments left by other users.
This post might seem useless for experienced people but I think it can help other people like me who have no real experience in soldering.