A baby can begin eating cucumbers by the time the baby reaches 9 months of age.
Although babies do eat most solid foods by age 6 months of age and up the baby should not be served or given cucumbers until at least 9 months of age.
Some foods that babies can choke on are hot dogs, raw vegetables, nuts, seeds, chunks of meat and cheese, whole grapes, popcorn, gooey candy or other candies, and chunks of peanut butter are all things a baby can choke on.
However when cut up properly or pureed the baby can eat anything except whole nuts, honey and raw shellfish.
Babies that are at least 6 months of age or older can have toast, butter on toast, cut up hotdogs, cut up cheese, cut up meat, etc.
As long as the baby has some teeth and is seated and in a highchair or other baby chair and they are supervised they can eat most foods that adults eat as long as they have the teeth for it and are on solid foods.
Cut up any food that may be too large for them to safely eat and always watch them while they are eating to avoid them choking.
Also you should know what to do when a baby or toddler or anyone is choking and if they are choking you should call 911.