Create Matched Filter Reference Signal when Scaling Unknown
I think the problem is not as bad as you suspect it is.

I wasn't around at the time, but from what I've read, early radar systems essentially connected the matched filter's output to an oscilloscope, and a trained operator would look at the phosphor and decide, from experience and intuition, when the signal raised above the noise ("the grass") indicating a reflection.

In practice, you never know in advance the amplitude of the pulse you're looking for. There is attenuation in the channel that can change over time, even on very short time scales. Sometimes you don't know how much power the transmitter is using.

There are at least two solutions to this problem. One is to use automatic gain control in the receiver, so that you know in advance the power or the peak amplitude of the pulse going into the matched filter. The second is to use a training sequence or a pilot signal, so that the receiver can calibrate the thresholds appropriately.

To add a bit of detail: to simplify the math, assume the signal $p(t)$ is time-symmetric and has energy 1. The transmitter emits signal $kp(t)$, with $k$ unkown at the receiver. The receiver correlates the received signal with a matched filter with impuse response $lp(t)$. When the transmitted signal is present at the receiver, the matched filter's output is $$r=kl+n,$$ which is a Gaussian random variable with mean $kl$ and variance $N_0/2$.

When nothing but noise is present at the receiver, the matched filter's output is just $$r=n,$$ which is a Gaussian random variable with mean 0 and variance $N_0/2$. If the receiver can estimate $l$, then the problem reduces to standard hypothesis testing (see for example these notes).