The first exercise that comes to mind for most people when in comes to lower body strength is the barbell squat. Of course, there are an extreme amount of benefits to this exercise, however overloading the spine prematurely for individuals who might not efficiently be able to can compromise gains.
There are certain variations to the squat to help the appropriate person increase their lower body strength without compromising form and health, and that will progress them efficiently and quickly.
The Racked Squat, and this Split Squat variation are potential options for you IF you are adamant about improving your squat strength, but don’t want to overload too quickly.