If they had warning and fast reflexes, it's possible that an ATGM couldn't catch them. For example, taking a "Javelin-like" ATGM - diameter is 0.14 meters, projectile initial mass 11.8 kg, with a presumably solid rocket that provides 570 newtons thrust initially, increasing to 770 newtons at 1.8 seconds and tailing off after that and balancing it against my 800 Dton spherical starship modeled such that it produces thrust that would give it 1g acceleration without air resistance, putting the whole thing at 100 meters elevation and then firing the ATGM at the starship when it is 1 km distance and giving the starship 1 second reaction time [which presumes automatic launch detection and evasion] at which point it accelerates away from the launch point and you get something like this:
I don't know what the drag coefficients of a Javelin are, so used 0.2 most of the time and 0.3 for the transonic region - probably not important as it doesn't get past Mach 0.42.
It's an interesting problem, something light enough that a person can carry is going to have to devote mass to either warhead or propellant. Shooting at something armored and slow means you should choose warhead, shooting at something fragile but fast means you should choose propellant. A starship is armored and fast, which I think would somewhat limit the options for a man-portable TL6 device to attack while it is in flight.
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