You will have to connect your soundbar elsewhere in your system. It could be an Audio Amp, A/V Receiver or any other device with a sound output.
Would a switcher or a splitter box do the trick?
No. The TV doesn't output anything. You need to connect your output device to the soundbar. Either cable box, DVD Player, etc. All of them will have a separate audio output aside from the HDMI or Component cables you use to plug them into the TV.
Connecting to the TV is impossible, as you said no audio outputs.
If you use a cable box (and/or a blu ray or dvd player) for a signal those usually have an optical out that you can plug into many soundbars and all home theater systems. That would be your only way.
You will have to connect your soundbar elsewhere in your system. It could be an Audio Amp, A/V Receiver or any other device with a sound output.
Would a switcher or a splitter box do the trick?
No. The TV doesn't output anything. You need to connect your output device to the soundbar. Either cable box, DVD Player, etc. All of them will have a separate audio output aside from the HDMI or Component cables you use to plug them into the TV.