Man-portable air-defense systems have been around for decades, and so have been anti-satellite weapons. But while the former is a small, short range rocket, the latter is as big as a cruise missile. Obviously, it is impossible to make such a small rocket go high enough to threaten a satellite.
Or is it?
Satellites are fragile, have a predictable orbit they cannot meaningfully alter, and have no counter-measure. So the rocket doesn't need acceleration or agility beyond what is needed to reach a specific point at a specific time. The launch itself can be timed to the second.
The smallest orbital rocket to be built was big enough to require a truck, but we aren't trying to reach orbit, only orbital altitude, which requires several times less fuel - which is why sounding rockets attempting to reach space are so much smaller than orbital rockets for the same payload. And we don't even need a payload, only to hit the satellite. Unless, of course, a small explosive charge gives the resulting cloud of debris a better chance to hit than the same mass in sensors and guidance.
So the question is, can an anti-satellite rocket be made small enough to fit a man-portable rocket launcher?
The total package must be, if possible, less than 35kg and small enough to be carried as a backpack. Or, if impossible, to be carried in separate components by the smallest possible team.
It must at least reach low orbiting satellites, so let's say 250 km minimum altitude for a vertical launch. The higher the better, though, both to give more launch sites and to reach higher satellites. We can even go for a range of rockets with varied capabilities. Being able to hit the ISS at a bit more than 400 km altitude would be great for advertising.
The fastest the setup on launch site the better, up to a few hours. More time can be spent setting parameters up in advance, though. Simpler setup procedures are also better, but not mandatory, as skilled operators can be trained anyway.
It must require no fixed infrastructure, not even a perfectly flat ground. If fueling is required, the fuel reserve must also be man-portable. Same thing for ground-based sensors or a ramp.
Toxic fuels should be avoided if possible, but if it can't be then something must be included to protect the crew during storage, transport, setup, and launch if they have to be close. Also there is toxic and toxic. White fuming nitric acid may be manageable, but chlorine trifluoride is right out.
it must be possible to store the components in standard warehouses for long periods, so corrosive, unstable or cryogenic fuels are to either be avoided or extra step must be taken for them.
The higher chance to hit the target the better, but less than 100% is acceptable. Let's avoid going below 50% if possible, though.
Don't worry too much about R&D cost or legal concerns, assume I am an evil billionaire with my own island lair and a plan to Conquer the World!, and I bought a few missile and aerospace companies to tap their skills and cover up the tests. I don't have access to nuclear materials, though, nor metallic hydrogen (whether it works out).
On the other hand, once mass-produced, the individual units should not be too expensive. Let's say less than a million dollars.
Assume the starting date you want from the 1960 up. Before is better, but if you need experimental tech like ramrockets or even fancy near-future tech like rotating detonation engines, so be it. Please don't go too far in the future, though.