That is indeed the Tradition, that Mary was resurrected and immediately assumed into heaven. Unlike Christ who still had things to do for 40 days, Mary went straight to heaven body and soul.
Apochryphal works written as early as 160AD imply same but these are hardly conclusive sources.
It seems an established orthodox theology along these lines was well established by 460AD as implied by the Euthymiaca Historia.
Here is related a report that the Christian Emporer Marcius asked the Patriach of Jersualem for the remains of the Virgin. The embarrassed Patriach had to correct the Emporer’s understanding - the Virgin’s remains were not kept anywhere because her tomb was found empty 3 days after her death.
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