You may want to consider going "simple" at first with costumes. If the costumes are too elaborate they take up a lot of time with on and off etc.
Large squares or colorful fabric with a stretchy elastic headband to keep them on are easy and quick and don't take up a lot of room. Children will respond well to a simple headpiece to suggest the character, or even start collecting hats.
Old bath robes (garage sales, Goodwill,??) also make good Biblical costumes.
Have kids make "costumes" from grocery bags: Invert the bag (open end down), cut out front panel of the bag. Cut a neck opening in the "bottom" of the bag. Decorate the bag with whatever. Cut arm holes in the sides of the bag. Kids wear the bag as a sort of "vest"
Also, you can contact your local schools, community theater, community college, etc to see if they have things they are ready to recycle.
Last, put a plea in your bulletin/newsletter and ask your congregation for help. There are still people out there who love to sew.