Well the first year of the Iraq War cost the US $54 billion, according to congress's budget[0]. This doesn't include the total cost of the supporting infrastructure need to be able to deploy troops in Iraq quickly, but we can estimate that using the increase in defence budget from 2002-3, or $94 billion ($132B in 2020)[1].

According to Wikipedia, Minuteman III ICBMs have a 2020 unit cost of $20 million[2], so for the cost of an Iraq invasion, the US could have fired about 6600 missiles. Considering the invasion toppled the Iraqi government, it's pretty unlikely that firing 6600 missiles with conventional payloads would have been anywhere near as effective.

[0]: https://en.wikipedia.org/wiki/Financial_cost_of_the_Iraq_War...

[1]: https://en.wikipedia.org/wiki/Military_budget_of_the_United_...

[2]: https://en.wikipedia.org/wiki/LGM-30_Minuteman#Counterforce