So what would you guys start building early against a Singed top while playing Olaf?

Mercs.
Phage -> mallet OR Hexdrinker.-> maw
(Get both eventually.)
Wriggles for insane lane sustain. (See what i did there?)
or, just a vamp scept => lategame zekes.

EDIT I stress that you need the most MS against a singed as possible, and as early as possible.

Boots 3
2 Dorans blades
Phage Or Hexdrink if you are doing bad.
Upgrade to merc treads if you are having problems/Iodic if you are doing extremely well
Then you should be near the end of laning phase.

Mercury's Treads, Wriggles, Hex to Maw if his damage still hurts, Phage to Mallet if you need health and a slow, Kindlegem to Shurelia's if laning isn't over. If you're still laning after that TAKE SOME TOWERS XD.