How can it be deduced that metallic zinc and metallic lead displace hydrogen from strong acid, whereas metallic copper and silver do not?

It is related to SRP(standard reduction potentials) or SOP(standard oxidization potentials) which we learn electrochemistry.
SRP is a scale which tells how well it is reduced.
SOP is a scale which tells how well it is oxidized.
The process 2H⁺+2e⁻→H₂ SRP at 25⁰C is 0
Metals such as lead and znic have lower SRP
{Zn²⁺+2e⁻→Zn SRP at 25⁰C is -0.76
and Pb²⁺+2e⁻→Pb SRP at 25⁰C is -0.13}
which means lead and znic have stronger reducing agent.
While metals like copper and silver have higher SRP.
{Cu²⁺+2e⁻→Cu SRP at 25⁰C is 0.34
and Ag⁺+e⁻→Ag SRP at 25⁰C is 0.80}

The hydrogen ion reacts better than copper and silver so they can't displace hydrogen(it is much more stable not to react).
Other metals such as gold, platinum, mercury also can't replace hydrogen.