The first requirement that must be satisfied to purchase a firearm in the U.S. is that the purchaser must either be a resident of a State within the United States or arrange for the licensed seller to directly export the firearm. From the Bureau of Alcohol, Tobacco, Firearms and Explosives web site:
A nonimmigrant alien without residency in any State may not purchase and take possession of a firearm. A nonimmigrant alien may only purchase a firearm through a licensee where the licensee arranges to have the firearm directly exported. A nonimmigrant alien who falls within an exception may, however, purchase and take possession of ammunition.
A nonimmigrant alien who has established residency in a State may
purchase and take possession of a firearm from an unlicensed person,
provided the buyer and seller are residents of the same State, and no
other State or local law prohibits the transaction. A nonimmigrant
alien with residency in a State may purchase a firearm from a
licensee, provided the sale complies with all applicable laws and
[18 U.S.C. 922(a)(9); 27 CFR 478.29a]
The licensee listed in the first paragraph who must "arrange to have the firearm directly exported" will need a license from the U.S. Commerce department for shotguns or from the U.S. Department of State for rifles and pistols. Additional licensing and customs authorizations would be required from the importing nation.
I answered a related question on travel stack exchange regarding possession of a firearm in the U.S. A foreign national who wishes to possess a firearm in the U.S. must be aware of the regulations regarding that possession. Note that possession doesn't mean owning; renting a firearm at a gun range or even sharing a gun at an informal range would constitute possession. Possession means in your control.
A foreign national who improperly possesses a firearm in the U.S. can be subject to significant criminal penalties as well as being banned from returning to the U.S.
As it relates specifically to Daniel Defense, they do have dealers in European countries and, assuming you are permitted to purchase such firearms in those countries, then you could indeed purchase a firearm made by Daniel Defense.