  We study primordial black holes (PBHs) formation in the excursion set theory
(EST) in a vast range of PBHs masses with and without confirmed constraints on
their abundance. In this work, we introduce a new concept of the first touch in
the context of EST for PBHs formation. This new framework takes into account
the earlier horizon reentry of smaller masses. Our study shows that in the EST,
it is possible to produce PBHs in different mass range, with enhanced power
spectrum, which could make up all dark matter. We also show that in a broad
blue-tilted power spectrum, the production of PBHs is dominated by smaller
masses. Our analysis put an upper limit $\sim\,$0.1 on the amplitude of the
curvature power spectrum at length scales relevant for PBHs formation.
