AtBeginLetter{enlargethispage{dimexpr 27.4mm-topskip relax}}

documentclass[]{scrlttr2}
usepackage{lipsum}
usepackage{showframe}

usepackage[footskip=20mm]{geometry}

setkomavar{firstfoot}{% do not remove this line end comment to prevent unintended indent
    Footer
}

KOMAoptions{
    enlargefirstpage % <- no effect
}

setplength{firstfootvpos}{250mm}

begin{document}

begin{letter}{Test}
%enlargethispage{dimexpr 20mm-topskip relax} % <- wanted result
opening{Hello}

lipsum[1-20]

end{letter}
end{document}

documentclass{scrlttr2}
usepackage{lipsum}
usepackage{showframe}

usepackage[footskip=20mm]{geometry}

KOMAoptions{firstfoot=off}% disables the default letter footer on the firs page
usepackage{scrlayer}
DeclareNewLayer[
  align=tl,
  hoffset=dimexpr.5paperwidth-.5useplength{firstfootwidth}relax,
  voffset=useplength{firstfootvpos},
  width=useplength{firstfootwidth},
  height=dimexprpaperheight-useplength{firstfootvpos},
  foreground,
  mode=picture,
  contents={putUL{raisebox{-height}{parbox{layerwidth}{usekomavar{firstfoot}}}}}
]{firstfoot}
DeclarePageStyleByLayers{firstpage}{firstfoot}

usepackage{xpatch}
xapptocmd{opening}{thispagestyle{firstpage}}{}{}% by default the first letter page uses page style empty

setplength{firstfootvpos}{250mm}

setkomavar{firstfoot}{% do not remove this line end comment to prevent unintended indent
    Footer
}
setkomavar{firsthead}{Header}% still works as expected

begin{document}
begin{letter}{Test}
opening{Hello}
lipsum[1-20]
end{letter}
end{document}