If you don’t have any sensors you could use, you could get the heading from the drive’s motor encoders. Typically you would use separate unpowered wheels for this, but it doesn’t look like you will be able to implement it in the short time you have. It won’t be as accurate though. This is the equation for finding the change in angle:
∆θ = ( ∆L - ∆R ) / ( S_L + S_R )
∆L and ∆R are the change in wheel positions in the left and right wheels and S_L and S_R are the left-right distances between the wheels and the center of the robot.
If you want more information, you can refer to these posts: