snapshot of solar system
You can get a position and velocity snapshot easily using the Python package Skyfield. It downloads a JPL Development Ephemeris and then interpolates the positions for whatever time you choose for your snapshot.

You can also use JPL Horizons to produce one or thousands of positions of solar system bodies.

This answer describes how to set up Horizons to save positions to your computer, and includes a script that can read the format of the saved tables. It also happens to be a simulator that does what you are talking about - statrs with a given position and propagates the orbits.