Within that framework, why do we assume the kaiju is indestructible? Being able to withstand large pressures and strains spread across the surface or joint is not the same as being immune to penetration attacks.
Elephants are big, bulky and have thick skin. A .50 cal still drops them because high mass, high velocity rounds are still VERY small in comparison to the surface they are striking. A surface that was designed to resist a broad force and stress, rather than a high force, small surface attack (like .22s penetrating bullet proof vests).
Because we are talking about something made of materials orders of magnitude tougher than elephants are. We're talking about tensile and compressive strengths not just in excess of those found in flesh, but in excess of those found in concrete and steel. Simply put, if it romps around trashing buildings apparently suffering no harm from that act, it must therefore be notably tougher than those buildings.
In any event, I'd like to see sciency refutation or support of the point that we are more likely to build a better bullet to kill a kaiju than a battle mech to kill a Kaiju.
Well, for the first appearance, there's no time to build anything - meaner bullet or mech. You have to use what is on hand. As noted, I figure the worst thing we can do to it is make it eat a fusion bomb.
What we do for the second appearance depends on what we learn from the first. If we vaporize the first monster with a nuke, we don't learn much, and we resort to building better bullets.
If we have a carcass, well, then maybe things change. Maybe we make some leaps and bounds in materials science, such that building the carbon-nanotube fiberglass the thing uses for flesh, or whatever it is, becomes a possible. Then, while better bullets may still be cheaper, the answer is in geopolitics, not physical sciences. Better bullets can be used on human hard targets a whole lot more easily than mechas. You can't hide the darned mecha on the move. It is big, and relatively slow. The nations of the world have deployed systems to detect big moving objects to find the kaiju, and they'll find mecha as well. You can't smuggle mecha, build them in secret, or secretly hand them off to third parties to use against your enemies. If you use it against another nation, everyone knows it. And that nation has its own mecha for defense.
In human terms, mechs are strategic, not tactical weapons, and are less dangerous than nukes, unless they become so cheap to build that they're as numerous as tanks or fighter planes.
How's that for an no-prize answer?