So, what we've got here: iPhone 5s 16 Gray, US GSM absolutely new. No sound from the earpiece on calls, etc. Sound ok on speaker and headphones.
What could it be?
Answers that proved to be wrong and what cannot be done (for some reasons).
1. Not the earpiece unit itself to blame - Have 2 similar handsets, swapped the earpiece units (thanks to iFixit tear-down guide, the speaker replacement is quite an easy procedure) works ok.
2. Not a software issue - restored both from a backup and as new, no results. Also turning bluetooth on/off, resetting and all other tricks found on Apple forums and here do not work.
3. No, the phone cannot be currently taken back to Apple for warranty.
4. Yes, I've removed the clear screen protection :)
Actually the sound can be heard, but on maximum volume it is no louder than a mosquito in an adjasent room, i.e. it is absolutely impossible to talk using the earpiece.
Thanks for your help!