Trust can absolutely be rebuilt but is requires effort of both parties; the betrayed party must be willing to give adequate time for trust to be restored and supportive of the process, and, the offending party must be willing to do the work and continue to do the work UNTIL the trust is restored.
Time and positive action is the key; a new relevant history must be created that outweighs the old relevant history and this is a process that canNOT be put on a timeline so patience and sincerity on the part of both parties is required.