If you are seeking a green card (U.S. lawful permanent residence) through marriage to a U.S. citizen or resident, one of the first requirements is that the marriage be legally valid in the state or country where it took place. It must comply with local laws and receive official government recognition (which you will have to supply a copy of as part of the process of applying for a green card).
In the case of a proxy marriage, however, there is an additional requirement. Even if it is considered legally valid in the place where you were married, U.S. immigration law will not recognize it unless it was later consummated (the two spouses had sexual relations).
According to the Adjudicator's Field Manual, published by U.S. Citizenship and Immigration Services (USCIS), at Section 21.3, "Consummation of a marriage can only occur after the ceremony, there is no such thing as "pre-consummation" of a marriage."
A proxy marriage occurs when either one or both matrimonial parties are not present at the marriage ceremony. Another person stands in for the bride and/or groom, as a "proxy," who says the vows and so forth.
That arrangement is exactly what the Immigration and Nationality Act (I.N.A.) prohibits in its language at Section 101(a)(35), stating that, "The term 'spouse,' 'wife,' or 'husband' does not include a spouse, wife, or husband by reason of any marriage ceremony where the contracting parties thereto are not physically present in the presence of each other, unless the marriage shall have been consummated."
Common situations where a couple choose a proxy marriage include where a member of the United States military is deployed overseas but wishes to marry without waiting for his or her next trip home; or where one member of the couple cannot travel, but they need or want to get married sooner rather than later.
USCIS will deem the marriage to have been consummated if both members of the couple were in the same place at the same time at some point following the wedding. You do not need to provide more personal evidence of the marriage having been consummated.
You will, however, need to provide plenty of evidence that the marriage is bona fide, not a sham to get a green card. In fact, U.S. immigration authorities are likely to demand more evidence of this fact from you than of most couples, because your marriage is already unusual, and you might not have spent much time together as a couple.
For more information, see Proving a Bona Fide Marriage for Immigration Purposes.