There is one base defence mechanic that was not yet mentioned: If one mission detects your base but fails to attack it, the next mission will not send search Ufos but immediately send the attack Ufo. This happened to me with the ambulances. The ambulances detected my base, but I could shoot them down before they reached it. Later, a ratmen harassment spawned in the same region and proceeded right to the attack run, as the base was already flagged as "detected". There were no ratmen patrols to warn me of the attack.
I just asked if there was a way to save my base without reloading some old save
What answers were you hoping for? You have a base where you cannot put troops and base defence is not finished.
Sooo... besides cheating, intercepting the attacking Ufo is the only option. However, most base attacks use Ufos for the assault that are designed to be unstoppable, either by having ridiculus speed or big size. For example the ratmen do a foot assault. You are not supposed to be able to intercept this, but because of game mechanics a Ufo needs to be spawned for the attack to happen. The solution is a "fake" Ufo with ridiculous speed that is interpreted as a comm signal. If it is one of those, you cannot stop the attack.
If you are doing a challange run it is not your first playthrough. Then you should know this mod has scripted early base defence missions. The ambulances looking for your base are guaranteed to show up in april of the first year. If you don't research the hideout search order, they will show up again a few month later. They pick a base at random, so there is a good chance your newly built base will be a target. Even if the new base did not do anything and it is just a hangar. Because of this mechanic, building a new base at the end of march is unadvised. The ambulances are slow enough that you can shoot them down though (if you can detect them). There are several more of these type of missions (ratmen harassment, Necropirate harassment, etc.) that start quite early, so leaving a base blank is always a risk.
The burrow is cheap, builds fast, has housing AND vault space. You can build over it. It is a very cheap and convenient one building solution to enable a defence force in a base. The mod makes it very easy for you to have defenders at your base. If you don't build a burrow in a new base, I would simply call it bad strategy. Because the build over mechanic saves you build time, I tend to spam burrows in all my bases. If you say you cannot beat the attackers because you chose to limit yourself to muskets, well... Challange means you wanted a higher chance to loose stuff.
I was just burnt out from base defences after that, as those are so long. I get combat stress per turn, too.
You choose to do a challange and then complain that the fighting is not fun / gets tougher?