。
I hope you had a happy birthday.
Literal
Good birthday [object-を] welcome-could-have [quotative-と] think [polite-ます].
迎える ('to welcome, receive, greet a time period') is the verb for 'meeting' or 'welcoming in' an event. 迎えられた is the passive/potential form — here carrying the 'was able to welcome' reading. ~と思います softens it to a polite wish/assumption.