If it were possible to work around the limitation by simulating touches, we would have done that already. Unfortunately it's not possible.
You should be able to play sounds at any time after the first touch. Only music can't play until the next touch after it's started. There's really nothing that can be done about it, it's a stupid limitation in both Safari and Chrome for Android. If you categorise the audio as a sound instead, it can play any time after the first touch, but then that fully decompresses the entire track in to memory which is pretty wasteful, whereas music can stream. So the restriction is completely pointless and encourages wasteful workarounds, but browser makers won't seem to budge on this.
TBH I would just ignore the limitation and let the engine do its workaround where music starts on the next touch after playing. You don't really need any "touch to continue" screens, it just won't start music playback until the user touches the screen, and if they're doing that a lot in your game hopefully they won't notice.