Try adding a Fade In node from your audio component. Read more here: Fade In | Unreal Engine Documentation
You’ll want to keep a reference to the audio component that you’re playing so you can trigger a Fade Out when necessary Fade Out | Unreal Engine Documentation
I whipped up a quick example to check out. The biggest headache from working with a Level Blueprint > HUD is going back from the HUD > Level Blueprint. It would all be much easier to manage if you just created a new GameMode for menu activities. This way, you could create a PlayerController that can help with this.
So, say. I have BP_GameModeMenu, BP_MainMenuPlayer, MainMenu (level) and MainMenuHUD. The MainMenu (level) uses BM_GameModeMenu, which points to BP_MainMenuPlayer.
MainMenuHUD
BP_MainMenuPlayer
Perhaps a little overkill, but should get you moving!