's is a tricky construction, one which notoriously trips up native speakers on a regular basis.
There are three uses of the suffix s in English:
Contraction of is, has, etc. The correct construction is 's - Tom's going to... is a contraction of Tom is going to.... This is the form mentioned in the question, but it is not the form actually being used in the sentence.
Plural noun. The correct construction is no apostrophe, so s. There are many cats in the United States
Possessive. The correct construction is with an apostrophe, so 's - Tom's cat is in the United States. This is the form actually being used in the example sentence in the question. The upcoming visit belongs to Tom.
The use of an apostrophe in the possessive form came about because the possessive use to be written as -es in all cases, but early printers chose to omit the e and replace it with an apostrophe.
There is a folk etymology that the possessive 's was originally a contraction of "his", as in "Tom, his upcoming visit to the United States". While not correct, this idea can be a helpful way to remember that the possessive form uses an apostrophe.
To directly answer the question, then, the expanded form of Tom's visit to the United States would be Tomes visit to the United States, but this construction is never used any more.