There are a number of ways to do it, one (as you suggested) is to disable (or restrict) the over current protection at start up - as long as it's only a very short time it shouldn't damage the chip. It could be as simple as a capacitor on the over current line - which delays the over current signal!.
Another way is a surge limiter, feed the chip through a large resistor, calculated to limit the current to no more than 4A. This prevents the over current triggering, then, after a short delay, short the resistor out - this is commonly done in high power amplifiers with toroidal transformers, the mains transformer is fed from a large resistor which is then shorted out by a triac after a couple of seconds. If you need to limit at DC you could use a transistor, FET, or relay to short it out.