Our archdiocese puts no restrictions on the pastor, therefore it belongs to the pastor to determine when a child can be admitted
Here is the relevant Canon
Our pastor does take the ‘soon as possible’ pretty seriously. He has specified certain requirements to the parish catechists, and when they are met, and the child is at or past the age of reason, our pastor prefers that the parents make arrangements for he child to receive Holy Communion.
In the case of our daughter, she made her First Holy Communion just after Christmas.
There will be a general Mass in the spring that she would also participate in that will include others who made their First Holy Communion.
But our pastor, (and Canon Law) see no point in having a child be refused Holy Communion if they meet the requirements set down by Canon 914. In fact Canon 912 would prohibit my pastor from doing so.
Of course, if a diocese has Particular Law, then Canon 912 would come into effect and the child should not present themselves for Holy Communion.