Particle System doesn't play in the Game view without opening Scene view first when playing it through script

Reproduction steps:
1. Open the attached project "repro51549"
2. Open "SampleScene"
3. Enter Play mode
4. Select the Scene view, then the Game view again

Expected result: the red Particle System plays at step 3
Actual result: the red Particle System plays at step 4

Reproducible with: 2022.1.0a13, 2022.3.8f1, 2023.1.9f1, 2023.2.0b4
Not reproducible with: 2021.3.19f1, 2022.1.0a12

Reproducible on: macOS 13.4.1 (Intel)
Not reproducible on: No other environment tested