C172 student pilot on a solo flight reported loss of control during landing resulted in runway excursion.

Narrative

I was student pilot conducting a solo flight where I had planned on staying in the traffic pattern to practice crosswind landings in a C172 as part of Checkride preparations. At the time of departure; the winds were slightly variable; but generally hovered around 250 at 4 kts - almost a direct left crosswind for the departure runway XX. This wind was just under my personal minimums of no more than 10 kts of headwind and 5 kts of crosswind.I departed from Runway XX and entered left closed traffic. On my turn from Base to Final I recognized that I was coming in high and should have gone around. Instead; I made the mistake of trying to still force the landing which caused me to come in faster than normal.During the course of the landing; I applied left aileron to correct for the wind (wing-low method); but most likely used too much aileron for the amount of crosswind that the plane was experiencing resulting in the plane drifting to the left. I tried to correct for this by applying the right rudder to align the nose of the plane with the runway; but the plane landed side loaded facing the left.I attempted to apply additional rudder and braking; but was unable to get the plane back onto the centerline and so it continued its rollout onto the left side of runway XX and into the grass field beside it.Luckily; the plane did not get stuck in the field; prop strike the ground; or sustain any other damage so after it stopped rolling I ran through the after landing and securing checklists; turned off the plane; and contacted a nearby CFI for further assistance. Both the plane and myself suffered no injuries or damage.There are two main takeaways from this:1. I should have gone around. There was no reason for me to try and force the landing if the approach was unstable and faster than expected.2. Too much aileron relative to the amount of wind. I should have used smaller control inputs on the ailerons during the landing to account for the wind drift so that I had enough rudder to correct.