We did them from the start, in fact, cucumber sticks were one of my daughter's first foods at 6 months. Some of the harder things they might not really be able to chew until they have molars, which is usually after 1. But no harm offering it and seeing what they can do. My daughter now often grabs a whole carrot out of the basket of veg on the shelf in the kitchen and eats it! She's almost 2 now, but she's been eating whole cucumbers since probably 16 months. If it's cut to a more manageable shape, they certainly will be able to handle it more easily from much younger.