Don't know exactly what sort of lifter arrangement you have on the SOHC on a
Toyota.
SOHC and DOHC engines may have cam followers instead of lifters  and, if so,
as long as the
clearances are adjusted properly and you have lubrication, there is not much
else you can do.

Do you know if your valve lash is adjustable, and if so have you set them
lately?

Oil pressure delay can be another issue when an engine is cold or drained
down.

My wife's car makes a bit of noise when it is cold, and it seems to be
associated with the
air path into the FI plenum, sort of like the old choke heat mechanisms.  I
havent been any
further with it when I found that it seems to be natural to the operation of
this car.