Hello. I can also report the same issue, including in the current beta.
The explanation that the first keypress is "waking up Cortana" doesn't seem right, because my experience is that the first letter appears as the SECOND letter when I type quickly.
For instance, if I click start and then type netsh
...what appears in the search box is entsh
It is never "eating" the first letter in my experience, it is delaying the first letter and inserting it late -- so it becomes the second letter. I can readily reproduce this behavior.
Very frustrating for a fast typist.
Thanks in advance for a genuine solution. Perhaps Start10 needs to collect more letters and then forward them to Cortana in the proper order.