\(\text{The letters A through G can be coded as 0 through 6}\\ \text{and thus a 3 letter set is equivalent to a 3 digit base 7 number}\\ \text{There are }7^3=343 \text{ such numbers and thus 343 sets of initials}\)

There are 7 possibilities (A~G) for the first letter, 7 for the second, and 7 for the third. Multiplying this together, we get 7^3=343 total ways to make a set of 3-letter initials.