Other than just doing the usual political pressure and PR dance to try to affect how the Legislature decides to redistrict (I believe in all of these states the Legislature is in control; some states use independent or otherwise non-partisan commissions), yes, you could sue under the VRA, though the success of such an effort is hard to gauge.
Your whole concern is conjectural, as full Census data is not yet available and legislatures cannot formally begin redistricting until they have the full data. We simply don't know if there would be any solid basis to push for one or more majority-minority districts under the VRA. And any such suit will have to wait until after the relevant state legislature has passed the law for its redistricting. The statistical realities and political pressures may already lead the legislature to create one or more such additional districts, potentially mooting your issue.
But for such an attempted suit, the controlling SCOTUS precedents here should be Thornburg v. Gingles (1986) and Cooper v. Harris (2017).
Thornburg v. Gingles created a three point (now expanded to four) test for determining if section 2 of the VRA required a majority-minority district be created:
- The racial or language minority group “is sufficiently numerous and compact to form a majority in a single-member district.”
- The minority group is “politically cohesive,” meaning its members tend to vote similarly.
- The “majority votes sufficiently as a bloc to enable it...usually to defeat the minority’s preferred candidate.”
- (added by Bartlett v. Strickland (2009)) A minority group must be a numerical majority of the voting-age population.
Cooper v. Harris held that section 2 of the Voting Rights Act does not require a numerical majority of voters in a particular district. Rather, it only requires that a compact and politically cohesive minority (satisfying the above; the third point seems particularly noteworthy) have the opportunity to elect its candidate of choice.
So to know if there's a solid legal case to push for additional such districts, one must demonstrate that the lack of them deprives a "compact and politically cohesive minority" satisfying Thornburg of the opportunity to elect its candidate of choice.
That a minority has insufficient districts, relative to its population proportion, where it is a majority is not a problem under the VRA, as if they are non-compact or non-cohesive, or not regularly defeated by the majority, then the act does not guarantee them such districts. And this is going to be a potentially thorny issue because a lot of the increases in minority populations seem to have occurred in densely populated, urban areas. It would be another, separate violation to try to just throw them all into one super-majority-minority district, so such areas are routinely covered by many districts. While compactness seems relatively easy to satisfy in a dense urban setting, the cohesiveness and ability to be frustrated by a cohesive majority population strike me as much harder to establish. I honestly haven't the foggiest clue how courts go about weighing the VRA compliance and general constitutionality of such districts, even with the Thornburg tests at hand.
For synopses of major redistricting cases, see this page created by the National Council of State Legislatures.