Ideally, with proper technique and mobility, you can expect to increase your strength in certain exercises pretty quickly. Now this doesnt mean you should bump the weight up significantly just because I said that is what should happen, but for me, usually, the 3rd and 4th weeks of getting back to an exercise see the biggest increase in strength.
I am talking about exercises such as squats and deadlifts mainly. After learning the proper technique for these exercises, along with having the ability to execute them properly, you should expect rapid increases in strength.
Personally, I find it counter productive to crush myself on a frequent basis, it is surprising how little volume you have to use with exercises such as squats and deads to improve strength dramatically, especially initially.
Many people think that ok if I crush myself this week with 8 sets of 8 using 225, next week I should be able to do 6 sets of 8 with 235, 240. Maybe, but I find it works better doing say, 10, 8, 6 and maybe 4, leaving a good amount in the tank on all the sets. The next week you may be able to add ten lbs to each set and have it be even easier than the previous week.
Giving us a video of yourself squatting would be very helpful as well.