Can a private company challenge an allegation made by the government and sue for damage? Let's say that you own a chocolate factory in Cuba, but you were blacklisted for allegation of using slave labor by the DOJ or DOC or the U.S. military, can you go to the U.S. and challenge the allegation in an U.S. court?
One approach would be to sue the government for defamation. Sovereign immunity limits your ability to file such a suit, though sometimes you can sue the government. Under the Federal Tort Claims Act, there is a limit on the causes of action which is more stringent than ordinary liability. In particular, you can sue for
Any other civil action or claim against the United States, not exceeding $10,000 in amount, founded either upon the Constitution, or any Act of Congress, or any regulation of an executive department, or upon any express or implied contract with the United States, or for liquidated or unliquidated damages in cases not sounding in tort, except that the district courts shall not have jurisdiction of any civil action or claim against the United States founded upon any express or implied contract with the United States or for liquidated or unliquidated damages in cases not sounding in tort which are subject to sections 7104(b)(1) and 7107(a)(1) of title 41.
Or, in short, "if the government does something illegal". There is no federal defamation statute (regulation etc) so it's not "against the law" in this specific sense for the government to defame you. And that assumes that there was a defamatory claim.
Whatever you mean by "blacklisting", it has to reduce to some restriction on commercial transactions under some regulation, such as the sanctions against Iran. Such restrictions are authorized by Congress, and generally involve a presidential order pursuant to a federal determination of unlawful behavior by parties "over there". For example, Huawei has been "blacklisted", but not all goods from China are blacklisted. Here are the current Cuba sanctions. Since this is a fairly broad and hypothetical question, let's assume that a company is on a list because of X, but X is not actually true. Then putting the company on the list is not legal (the statutory conditions are not satisfied), and the company can sue the government. But hire a really good attorney, because the underlying authority may involve "sole determination" or "at the discretion" of the President.
Products produced with forced labor (even in part) cannot be imported. The legal details regarding that restriction are here, but basically there may be an investigation into an allegation of forced labor. AAnd then
(f) If it is determined on the basis of the foregoing that the merchandise is subject to the provisions of the said section 307, the Commissioner of CBP, with the approval of the Secretary of the Treasury, will publish a finding to that effect in a weekly issue of the Customs Bulletin and in the Federal Register.
(g) Any merchandise of a class specified in a finding made under paragraph (f) of this section, which is imported directly or indirectly from the locality specified in the findings and has not been released from CBP custody before the date of publication of such finding in the Federal Register shall be considered and treated as an importation prohibited by section 307, Tariff Act of 1930, unless the importer establishes by satisfactory evidence that the merchandise was not mined, produced, or manufactured in any part with the use of a class of labor specified in the finding.
You might sue under the theory that required procedure wasn't followed; you might even sue under the theory that no reasonable finder of fact could think that the goods were the product of forced labor. However, the courts generally defer to the judgment of regulatory agencies, so you will probably lose that lawsuit. But also, you would not be suing over the allegation, you would be suing over the restriction. The government can allege away to its best judgment, however bad that may be.
Let's say that you own a chocolate factory in Cuba, but you were blacklisted for allegation of using slave labor by the DOJ or DOC or the U.S. military, can you go to the U.S. and challenge the allegation in an U.S. court?
You cannot successfully sue the government (or government officials acting in their official capacity) for money damages for intentional torts (including defamation, but excluding certain civil rights violations) in court due to their sovereign immunity.
You can generally sue for injunctive or declaratory relief to be removed from a formal government classification that has legal consequences (e.g. forbidding you from bidding on U.S. government contracts). Most such statutes have a formal process for doing so, but if the statute does not, you can still sue in an ordinary court case of that government's courts. There are often significant procedural limitations on such lawsuits (such as short statutes of limitations and a requirement that administrative remedies set forth in the statue or regulation be exhausted).