Remedy for agencies unconstitutioal actions
Yes, the US government must agree to be sued; it's a concept called sovereign immunity.
There is a remedy for unconstitutional actions by a federal agency:
U.S. Supreme Court
LUJAN v. DEFENDERS OF WILDLIFE, 504 U.S. 555 (1992)
“Over the years, our cases have established that the irreducible constitutional minimum of standing contains three elements. First, the plaintiff must have suffered an "injury in fact" - an invasion of a legally-protected interest which is (a) concrete and particularized, see id., at 756; Warth v. Seldin, 422 U.S. 490, 508 (1975); Sierra Club v. Morton, 405 U.S. 727, 740 -741, n. 16 (1972); 1 and (b) "actual or imminent, not `conjectural' or `hypothetical,'" Whitmore, supra, at 155 (quoting Los Angeles v. Lyons, 461 U.S. 95, 102 (1983)). Second, there must be a causal connection between the injury and the conduct complained of - the injury has to be "fairly . . . trace[able] to the challenged action of the defendant, and not . . . th[e] result [of] the independent action of some third party not before the court." Simon v. Eastern K. Welfare [504 U.S. 555, 561] Rights Organization, 426 U.S. 26, 41 -42 (1976). Third, it must be "likely," as opposed to merely "speculative," that the injury will be "redressed by a favorable decision." Id., at 38, 43.
The party invoking federal jurisdiction bears the burden of establishing these elements. See FW/PBS, Inc. v. Dallas, 493 U.S. 215, 231 (1990); Warth, supra, at 508. Since they are not mere pleading requirements, but rather an indispensable part of the plaintiff's case, each element must be supported in the same way as any other matter on which the plaintiff bears the burden of proof, i.e., with the manner and degree of evidence required at the successive stages of the litigation. See Lujan v. National Wildlife Federation, 497 U.S. 871, 883 -889 (1990); Gladstone, Realtors v. Village of Bellwood, 441 U.S. 91, 114 -115, and n. 31 (1979); Simon, supra, at 45, n. 25; Warth, supra, at 527, and n. 6 (Brennan, J., dissenting). At the pleading stage, general factual allegations of injury resulting from the defendant's conduct may suffice, for on a motion to dismiss, we "presum[e] that general allegations embrace those specific facts that are necessary to support the claim." National Wildlife Federation, supra, at 889. In response to a summary judgment motion, however, the plaintiff can no longer rest on such "mere allegations," but must "set forth" by affidavit or other evidence "specific facts," Fed.Rule Civ.Proc. 56(e), which for purposes of the summary judgment motion will be taken to be true. And at the final stage, those facts (if controverted) must be "supported adequately by the evidence adduced at trial." Gladstone, supra, at 115, n. 31.
When the suit is one challenging the legality of government action or inaction, the nature and extent of facts that must be averred (at the summary judgment stage) or proved (at the trial stage) in order to establish standing depend considerably upon whether the plaintiff is himself an object of the action (or forgone action) at issue. If he is, there is ordinarily little question that the action or inaction has [504 U.S. 555, 562] caused him injury, and that a judgment preventing or requiring the action will redress it”
