I am not familiar with the particular steels you listed because they are not prequalified per AWS D1.1. However, it is the high strength quench and tempered steels that should not be examined right away since they are more susceptible to delayed cold cracking due to hydrogen.
Al
Since the base metals you note here appear to be "unlisted" in D1.1, I think the decision on when to perform the NDT should be determined by the Engineer.
Also since the base metals require Procedure Qualification, this is something the engineer should determine prior to performing the procedure qualifying weld tests.
The S460G2 sometimes requires PWHT so that's something to think about.
D1.1 Table 6.1 (5) Time of inspection does list some circumstances that require a hold point of 48 hours. If your unlisted material is similar to those base metals, your engineer should be able to evaluate and direct you.