According to HP Specification, your Elitedesk 705 G4 uses an older B350 chipset board, which would require a BIOS update to support AMD Picasso generation processors like the 3400G.
However the BIOS Version History only mentions Bristol Ridge (A-series) and Pinnacle/Raven Ridge (2000-series) processors, there is no mention of Picasso (3000-series) support.
Typically on those older chipset boards, the later AGESA code to support Picasso would require removing support for the early Bristol Ridge processors, so I suspect HP has not made the newer code available.
You could try contacting HP Support but it does not appear it will work.
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