I just leave the reproduction method using a new project here so that other users can know it and won't report it again.
1. Create a new Basic Scene.
2. Create a Particle System.
3. Change the Simulation Space to 'World'.
4. Change the Culling Mode to 'Pause'.
5. Move the Particle System away from the Main Camera's view (e.g. Position 0, 0, -20).
6. Start Play mode.
7. Use the Inspector to move the Particle System into the Main Camera's view (e.g. Position 0, 0, 0).

Expected result: Particles are shown in the Game view.
Actual result: No particles are shown.

Note:
- If the Scene view and the Game view are split in the editor, you should also make the Particle System leave your Scene view (e.g. just pan) before starting Play mode.
- After starting Play mode, if you switch to the Scene view and look at the Particle System, the simulation resumes. It seems that the resuming logic depends on the Scene camera but not the Main Camera.
- If you build the project and run it, there is no Scene view so the simulation will never resume. But in this way, you need a script to move the Particle System. Please note that you should not move it into the Main Camera's view too early (i.e. in the first frame). Otherwise, the simulation will not pause.

It is just a tiny problem. The current alternative is setting the Culling Mode to 'Always Simulate'. But I still hope it can be fixed one day.