The World Health Organization reports that the average weaning age is 4.2 years worldwide at present, however the weaning age has declined in modern times and the weaning age would have been higher in the past.
This is supported by the book of II Maccabees, 7:27 wherein a mother casually mentions giving milk to her son for three years which would be consistent with Samuel being about 3-5 years of age when he was dedicated at the temple and consistent with present and historical averages.
Leaning over her son, she fooled the cruel tyrant by saying in her native language,
My son, have pity on me. Remember that I carried you in my womb for nine months and nursed you for three years. I have taken care of you and looked after all your needs up to the present day.
Therefore, Samuel was probably older than 3, but there is no proof of this. We can only guess based on historic and anthropological data and trends and context. This also assumes this occurred relatively soon after weaning since technically a teenager would be dedicated "after weaning" too, though it would be an odd milestone to note if dedication occurred much later than the time of weaning and there was a significant gap between.