"Climbing" small steps in 23mm tires
First of all, to reinforce what Daniel pointed out, do NOT approach such an obstacle at an angle unless you want to eat pavement. Hit step ups, step downs, and especially railroad tracks as perpendicularly as possible. If it's a right turn you're taking, assuming you're in a country that drives on the right side of the street, signal, take the lane, and take a wide turn so you're hitting the lip at a 90 degree angle or close to it. Left turn you should offer you a little more room. That's the first half of hitting such an obstacle safely without dismounting from the bike.

Part two: if you want to get over the step "as safely as possible" then you want to hit it as slow as possible. That's great if you're not in traffic, but even if you aren't it sucks to lose your momentum. What you need to practice is something akin to a bunny hop, however having both wheels leave the ground simultaneously for small bumps typically isn't necessary. Practice pulling up your front wheel and immediately after gravity takes back over pulling up your back wheel with your feet and legs. Practice this in your driveway or on a quiet street over small obstacles. As you become comfortable with this maneuver you can practice on bigger obstacles and at higher speeds. If and when you feel comfortable to do so you can hop both wheels at the same time at high speed- whatever you feel comfortable with.

How big an obstacle you can handle totally depends on how comfortable you are with doing this and how high you can pull the wheels off the ground.