An RC low pass filter on your bandgap core's output, before
the error amp sees it, can be tolerably compact and give you
a reasonable soft-start dV/dt. But what's reasonable, to who,
that wants some digging - opinions surely vary, as they have
to do with input supply capability and all decoupling attached
to the LDO's output. Nobody wants a huge current slug but
a lot of people want no more turnon delay or slowness in
reaching final value, than necessary. But hard to get customers
to give you good quantitative guidance for these "abnormal
operation" type things, unless they've got bite marks to show.
You may want to add some explicit discharge to the vref
delay capacitor, run it off the UVLO function (which needs
a different branch of the vref, without such stuff) for the
case that the upstream supply gets into some sort of
"hiccup" mode from other actors' inrush remands.