Android phone's may have manufacturer specific settings that limit notifications from appearing until you open Signal. Use the following steps as guidelines to navigate through settings for your specific phone.
Android phone Settings > Apps > Apps > Signal > Power Usage Details > App Launch > Set to Manage Manually and enable these options: Auto-Launch, Secondary Launch, and Run in Background.
Android phone Settings > Wi-Fi > Advanced > Always keep Wi-Fi on during sleep.
Android phone Settings > Device Maintenance > Battery > MENU > App Power Monitor > Disable or selectively choose apps to sleep from Settings > Device Maintenance > Battery. Make sure to exclude Signal from the sleep list.
Android phone Settings > Device Maintenance > Battery > Power saving mode > Disable ot adjust to MID.
Android phone Settings > Battery > Unmonitored apps > Add apps > Signal > Done > Restart your phone.
Samsung 8: Android phone Settings > Apps > Menu > Special Access > Optimize battery usage > select the drop down which likely states ‘apps not optimized’ and switch to ‘all apps’ > find Signal and tap on the switch to turn it off.
Sony
Android phone Settings > Storage & memory > turn off the 'Smart cleaner' option or continue to tap the three dots at the top right > Advanced > add Signal to the whitelist.
Android phone Settings > Power management > Tap STAMINA mode > Apps active in standby > add Signal to the whitelist.
Vivo
Apps drawer > iManager > App manager > Autostart manager > allow Signal to auto-start in the background.
Android phone Settings > Additional Settings > Battery and Performance > Manage apps' battery usage > turn 'Power saving modes' off > open the Security app > navigate to Permissions > add Signal to Autostart > invoke Task Manager > find Signal > drag it downwards until the padlock icon appears.