The interaction of ultra-intense high-power lasers with solid-state targets has been largely studied for the past 20 years as a future compact proton and ion source. Indeed, the huge potential established on the target surface by the escaping electrons provides accelerating gradients of TV/m. This process, called target normal sheath acceleration, involves a large number of phenomena and is very difficult to study because of the picosecond scale dynamics. At the SPARC_LAB Test Facility, the high-power laser FLAME is employed in experiments with solid targets, aiming to study possible correlations between ballistic fast electrons and accelerated protons. In detail, we have installed in the interaction chamber two different diagnostics, each one devoted to characterizing one beam. The first relies on electro-optic sampling, and it has been adopted to completely characterize the ultrafast electron components. On the other hand, a time-of-flight detector, based on chemical-vapour-deposited diamond, has allowed us to retrieve the proton energy spectrum. In this work, we report preliminary studies about simultaneous temporal resolved measurements of both the first forerunner escaping electrons and the accelerated protons for different laser parameters.