Student pilot reported loss of normal brakes during landing roll out resulted in a runway excursion with no damage or injuries.

Narrative

On a student solo XC (Cross Country) with Company flight school in ZZZ1. On approach to ZZZ; I set up to enter traffic pattern on a left downwind approach at a 45 for Runway XX. No issues entering downwind or turning base. I am in full landing configuration shortly after turning base as I have been taught. As I turned final; I notice I am a little high; so I power idle and pitch the nose down a little. On final with the nose pitch down towards the center runway numbers; my airspeed is about 76 kts. As I make my final call out to ZZZ traffic for short final; I transfer into ground effect. Was in ground effect a little bit past the 1;000 ft. markers while maintaining center line. As airspeed begins to bleed off; I pull back on the yoke gently to induce a flare as I am coming out of ground effect. My main gears make first contact with the runway and then the nose gear comes down. I still have control of the direction of the plane and maintaining center line. Shortly after landing; I try to apply brakes to slow down. At that point; I feel no tension on the brakes or no indication that me pressing down on the brakes is causing the plane to slow down. I take my foot off the brake pedals to reapply pressure and I still feel no tension or no indication that the brakes is slowing the plane down like in a normal landing. As I am continuing to reapply full pressure on brakes hoping that they will start working; I apply a little bit too much pressure to the left rudder while trying to get the brakes working again with no luck. The plane starts to turn a little to the left; I then add a little bit of right rudder to avoid turning too far left which causes the plane to skid to the left and then turn to the right. As the plane starts to turn to the right from me adding a right rudder; I then add a little bit of left rudder to regain control. As that happens; the plane skids a little to the right. These are not major inputs of rudder pressure to the left and right; but it was enough to cause the plane to skid on the runway in each direction as I try to regain control of the plane while causing the plane to somewhat slow down without the use of brakes at my disposal.At this point; I abandon the thought of the brakes working to cause the plane to slow down like brakes should do in a normal landing situation. I immediately shifted my focus to regaining control of the plane and safely coming to a complete stop with no damage done to the plane; airport; or myself. As the plane stops skidding to the right and maintains a straight path to the left side of Runway XX; it is still moving fast enough for me to conclude that the plane was going to go off the runway. Also; I know if I keep adding rudder inputs to try and keep it on the runway then I will continue to not have control without the use of brakes. With that in mind; the plane is on a direct path to the left side of Runway XX and heading towards a runway sign. If I would have kept going straight with the speed the plane was still going; I know for a fact that I would have run into the sign and caused damage to the plane; the airport; and possibly myself. With that in mind I just add a little bit of left rudder to turn the plane and avoided hitting the runway sign. I also concluded that the grass would help slow the plane down as I had no choice; but to let it roll in the grass to slow the plane down.As I am in the grass on the left side of Runway XX and avoided the runway sign; the plane is slowing down. It is still moving fast enough to run into what it appears to be high standing grass field or crop field. The height of the grass or crop field is higher than myself standing straight up on the climbing area of the right wing where you enter the aircraft from my observation. To avoid damage to the plane; I added right rudder to avoid the high grass/crop field and the plane turns to the right and comes to a complete stop. At this point; I am off to the left side of Runway XX away from potential danger of aircraft wanting to fly into the untowered airport. I immediately get on the CTAF to let ZZZ traffic know about the excursion; so they are made aware that there is no potential danger. Name; a CFI at Company; was in the area doing a training flight with a student pilot and contacted me on the CTAF to see if I was okay and safe. At the same time; other pilots on the frequency called in to see if I was okay. I informed the frequency that I was okay and safe. I gave brief explanation of what caused the excursions which was my brakes not working upon landing. Name told me that he was happy that I was okay and told me to complete the shutdown terminate checklist and immediately call my instructor; Name1; while Name proceeded turn around to come in and land to check on me. ZZZ personnel also drove over to see if I was okay and offered to help as I was talking to my Instructor on the phone for the next steps. Shortly after getting off the phone with my Flight Instructor; a representative from Company flight safety contacted me and advised me on the next steps.