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The AME will not use the GPU's Ray-traced rendering. You have two options, render to a production format to create a DI (digital Intermediate, my preferred method) then compress for delivery using AME or open your AE preferences and choose "Show Deprecated Formats in Output Module Settings" from the Output section of preferences, then render and live with single pass compression. It's better than it used to be but AME will give you a superior product for delivery.
I agree with Rick. I almost always render an intermediate file from AE and then use the Adobe Media Encoder to make my final file.
Another good reason to do this is that you can encode a number of different variations of the compression settings on your final video to test image quality vs. file size and such without having to re-render the whole AE project - you're just encoding off of a video file!
What Rick and Szalam recommend is what we recommend: render and export a master from After Effects and use Adobe Media Encoder to create deliverables. I use a watch folder in AME to make that automatic.