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What I think is happening is the Roku starts up at a 720p resolution that all HD sets can display. It then tries to switch to the resolution for your set, which entails a new negotiation of the HDMI connection parameters between the Roku and the tv. The blackout is most likely the time period necessary for this HDMI "handshake". Some sets will do this faster than others.
You might be able to speed up this handshake by setting your display type to the actual resolution of your set instead of the auto setting.
The other thing you can do is power your Roku using the power converter that came with it plugged into your house power instead of a USB port on your tv so that the Roku stays on. Repeated startups and shutdown are typically harder on electronics than just letting them run. The Roku will then be instantly available in the proper resolution when you turn on the set. This also enables the Roku to keep itself up to date by receiving updates when you're not watching anything. If you do this it is a good practice to return you Roku to its home page when done viewing so that it doesn't continue to stream when nobody's watching. When not streaming the power consumption is miniscule.
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Roku Streaming Stick+ 3810 | TCL Roku TV 43S245/C107X | Roku Streaming Stick 3600