While it's understandable that a crying baby can be stressful for parents and disruptive to others in a restaurant, it's generally not appropriate or advisable to hand off your baby to the restaurant staff, including the waitress, to babysit while you eat.
Restaurant staff, including the waitstaff, have their own duties and responsibilities to attend to, and it is not part of their job to babysit patrons' children. Additionally, they may not have the training or experience to care for infants properly, and it could be a liability issue for the restaurant if something were to happen while the baby is in their care.
If you find yourself in a situation where your baby is crying uncontrollably in a restaurant, here are some more appropriate steps you can take:
Take turns with your dining partner: If you're dining with someone else, take turns eating and comforting the baby so that one person can eat while the other tends to the child.
Step outside: If the baby's crying is disrupting others, consider taking the baby outside for a brief walk or change of scenery. Fresh air and a change of environment might help soothe the baby.
Use distraction: Bring some toys or other items that might distract and entertain the baby during the meal.
Be understanding: Understand that babies can be unpredictable, and sometimes, despite your best efforts, they may still cry. If other diners seem bothered, a brief apology can go a long way in showing consideration for their experience.
Order takeout: If your baby is particularly fussy, consider ordering your food to go and enjoy your meal in a more comfortable and private setting.
Remember that being a parent of a young child comes with challenges, and sometimes babies cry for reasons beyond our control. It's essential to remain patient and understanding, both with your child and with others around you. If possible, choose family-friendly restaurants or dining times that are less busy to minimize the impact of your baby's crying on other patrons.