I don't have specific experience myself, but the Good Food Company, which works with many preschools/daycares, offers a vegetarian menu. Glancing at the menu, it does seem pretty starch-heavy (lots of pasta variations) but options also include bean burritos, vegetarian chili, lots of fruit, falafel, and vegetable soups.
If you're open to in-home day cares, you might look at one that is run by an Indian provider, or someone else who would be very culturally familiar with preparing vegetarian foods. (Also, Indian food is yum.

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