Chuck Estrada signed his 1962 Topps, as well as the 1961, 1963 and 1965 Orioles team cards. He was the first player to sign the 1963 and 1965 team cards, although I already have them signed by Brooks Robinson, as a single-signed card.
I currently have a 1957 Orioles team card out to Brooks, which will be Brooks Robinson single-signed team card number seven for my collection. I have had him sign the 1958, 1961, 1963, 1965, 1971 and 1972 Orioles team cards.
The 1956 team card would be the earliest card that would make sense for Robinson to sign, since the 1956 card is commemorating the 1955 team, his rookie year. The team cards are always showing the team from the previous year, which can get a little confusing.
In 1955, Brooks Robinson appeared in 6 games with 22 plate appearances. He struck out in 10 of those 22 plate appearances! He didn't seem to be on a Hall of Fame trajectory.
His stats can be found at baseball-reference.com, of course.
And speaking of confusing, there's an interesting article on Sports Collectors Daily about the pictures used on the Topps team cards. In general, they were pretty lax about having an accurate picture. I suppose someone thought that the picture was so small that no one would notice if the team photo wasn't accurate.
They found that they used an old photo over 20% of the time! And they used a team photo from 1959 for the 1964 Pirates card. They also reused a 1959 Giants team photo for their 1966 team card! And most surprising, they used the same Dodgers team photo for their team cards from 1960 to 1965!
You can read the article here.
It's funny, and it's also kind of disappointing. I've had players refuse to sign a team card because they weren't in the picture. Now I wonder if it's because they knew the wrong picture was used, or if they assumed they weren't in it because they hadn't made the team yet, or were traded to the team mid-season, etc.
I send a team card to a player as long as they made at least one appearance for that team in that season. For example, if a pitcher got called up to play for the Giants for one game in 1962, I'll send them the Giants team card from the 1963 Topps set.
Time to quit talking, and start sending out requests...