Question

why do you think accurate measurements of time became possible much after accurate measurement of length and mass

Answer 1

Long ago, pendulum clocks were used. Time period of a pendulum is
             T = 2 π √(L/g)
if length is accurate, time period could be accurate.

Time is calculated using the physical quantities that depend on the length and mass of objects. Only when these quantities can be measured accurately, then time durations can be measured accurately.