Recently, the EMPRESS collaboration has included new data in the extraction
of the primordial $^4$He abundance from Big Bang Nucleosynthesis (BBN),
resulting in a determination that differs from the previous value and from
theoretical expectations. There have been several studies attempting to explain
this anomaly which involve variation of fundamental constants between the time
of BBN and the present. Since the Higgs vacuum expectation value (vev) is the
only dimensionful parameter in the Standard Model and it is already known to
vary during the electroweak phase transition, we consider the possibility that
the vev is slightly different during BBN compared to its present value. A
modification of the vev changes not only particle masses but also affects,
through mass thresholds, the QCD confinement scale. We use the recently
developed PRyMordial program to study this variation and its impact on the
$^4$He and deuterium abundances. We find that bounds on $|{\delta v}/{v}|$ are
approximately $0.01$, and that the EMPRESS result can be explained within
$2\sigma$ if $0.008 < {\delta v}/{v}< 0.02$, but at the cost of worsening the
current $2\sigma$ discrepancy in the deuterium abundance to over $3\sigma$.
