The Geordie striker, formerly of Liverpool and Newcastle, signed for Daggers last week - along with taking a share in the club as part of a Qatari takeover.
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However, Carroll won't be seen for six weeks due to injury and is out of Daggers' opening home fixture of the Enterprise National League South against Ebbsfleet United on August 9.
Daggers boss Lee Bradbury admits Carroll has collected a hamstring injury, stating: "Starting from the top of the pitch, obviously Andy (is out) with his hamstring.
“He is going to be four to six weeks. A massive loss for us.”