You need a "normally on" current, first. Then you need a
switch that applies it until output is up and stable, then
takes it completely away so as not to bother the core.
That's the tricky bit since many node voltages vary greatly
with process & temp.
While a diode-steered resistor can work, it often is found
to meddle at some corner or fail to boot at the opposite.
In later designs I've tended to use a hard switched hysteretic
control based on the bandgap voltage exceeding some
minimum limit. Where this limit lies, has to do with the
sub-operating-point loop gain, how far out can you be
and still snap-to the desired operating point under all
conditions?
That simple loop is probably fairly low gain.
Given that you are in a BCDMOS process I'd suggest
looking at a completely BJT based PTAT core. Then you
can probably find a lot of simple startup circuit art in
older IC design textbooks (blue binding Gray & Meyer,
etc.). But still beware the curvature or plain messed-up
contribution of a mis-scaled startup bleed.