You could volunteer at any age. Underage boys could enlist with the permission of their parents, but there are numerous examples of boys who ran away from home and enlisted in a Confederate organization. If the surgeon examined the boy and found him physically capable of field duty, he was in service. Parents had to go through the court system or appeal to a senior military authority to have him released.

Here's the section of the law (Feb. 17, 1864) concerning junior and senior reserves. The "minute-men" companies had to be formed within thirty days of passage of the act. Otherwise it would appear that this provision doesn't apply.

SEC. 5. That all white male residents of the Confederate States, between the ages of seventeen and eighteen and forty-five and fifty years shall enroll themselves, at such times and places, and under such regulations as the president may prescribe, the time allowed not being less than thirty days for those east, and sixty days for those west of the Mississippi river, and any person who shall fail so to enroll himself, without a reasonable excuse therefore, to be judged of by the president, shall be placed in service in the field for the war, in the same manner as though he were between the ages of eighteen and forty-five: provided that the persons mentioned in this section shall constitute a reserve for state defence and detail duty, and shall not be required to perform service out of the state in which they reside.

SEC. 6. That all persons required by the fifth section of this act to enroll themselves may, within thirty days after the passage hereof, east of the Mississippi river, and within sixty days if west of said river, form themselves into voluntary organizations of companies, battalions or regiments, and elect their own officers--said organizations to conform to the existing law, and having so organized, to tender their services as volunteers during the war to the president; and if such organization shall furnish proper muster rolls, as now required, and deposit a copy thereof with the enrolling officer of their district, (which shall be equivalent to enrollment,) they may be accepted as minute men for service in such state, but in no event to be taken out of it. Those who do not so volunteer and organize, shall enroll themselves as before provided, and may by the president be required to assemble at places of rendezvous, and be formed into companies, battalions and regiments, under regulations to be prescribed by him, and shall have the right to elect their company and regimental officers; and all troops organized under this act for state defence shall be entitled, while in actual service, to the same pay and allowances as troops now in the field.

SEC. 7. That any person who shall fail to attend at the place of rendezvous, as required by the authority of the president, without a sufficient excuse, to be judged of by him, shall be liable to be placed in service in the field for the war, as if he were between the ages of eighteen and forty-five years.