Make the position of the Earth at the midpoint in time (t=0) to be the origin.
The sun is now at [-1 AU, 0].
Move the Earth backwards from the origin by two Earth diameters (25,512 km).
Deposit a floating astronaut at [0, +2 Earth diameters] with zero velocity , but deny them any means of propulsion per the question's premise.
Now start and see what happens ...
Firstly, it's going to take a big rocket to do this (larger than any rocket we have built so far btw).
We're travelling together with the Earth, so our speed relative to the Earth is 0. Thus, this isn't really "coming to a halt", it's more like "speeding up" to 67,000 mph (30 km/s).
Does the Earth blur past at 30 km/s? Not really.