  Intermediate-mass black holes (IMBHs) are those between 100 and 10$^5$ solar
masses ($M_{\odot}$); their formation process is debated. One possible origin
is the growth of less massive black holes (BHs) via mergers with stars and
compact objects within globular clusters (GCs). However, previous simulations
have indicated that this process only produces IMBHs $<500 M_{\odot}$ because
the gravitational wave recoil ejects them when they merge with other BHs. We
perform star-by-star simulations of GC formation, finding that high-density
star formation in a GC's parent giant molecular cloud can produce sufficient
mergers of massive stars to overcome that mass threshold. We conclude that GCs
can form with IMBHs $\gtrsim 10^3 M_{\odot}$, which is sufficiently massive to
be retained within the GC even with the expected gravitational wave recoil.
