Objection 1. It seems that the character of Confirmation does not presuppose, of necessity, the baptismal character. For the sacrament of Confirmation is ordained to the public confession of the Faith of Christ. But many, even before Baptism, have publicly confessed the Faith of Christ by shedding their blood for the Faith. Therefore the character of Confirmation does not presuppose the baptismal character.
Objection 2. Further, it is not related of the apostles that they were baptized; especially, since it is written (John 4:2) that Christ "Himself did not baptize, but His disciples." Yet afterwards they were confirmed by the coming of the Holy Ghost. Therefore, in like manner, others can be confirmed before being baptized.
Objection 3. Further, it is written (Acts 10:44-48) that "while Peter was yet speaking... the Holy Ghost fell on all them that heard the word... and [Vulgate: 'for'] they heard them speaking with tongues": and afterwards "he commanded them to be baptized." Therefore others with equal reason can be confirmed before being baptized.
On the contrary, Rabanus says (De Instit. Cleric. i): "Lastly the Paraclete is given to the baptized by the imposition of the high priest's hands, in order that the baptized may be strengthened by the Holy Ghost so as to publish his faith."
I answer that, The character of Confirmation, of necessity supposes the baptismal character: so that, in effect, if one who is not baptized were to be confirmed, he would receive nothing, but would have to be confirmed again after receiving Baptism. The reason of this is that, Confirmation is to Baptism as growth to birth, as is evident from what has been said above (1; 65, 1). Now it is clear that no one can be brought to perfect age unless he be first born: and in like manner, unless a man be first baptized, he cannot receive the sacrament of Confirmation.
Reply to Objection 1. The Divine power is not confined to the sacraments. Hence man can receive spiritual strength to confess the Faith of Christ publicly, without receiving the sacrament of Confirmation: just as he can also receive remission of sins without Baptism. Yet, just as none receive the effect of Baptism without the desire of Baptism; so none receive the effect of Confirmation, without the desire of Confirmation. And man can have this even before receiving Baptism.
Reply to Objection 2. As Augustine says (Ep. cclxv), from our Lord's words, "'He that is washed, needeth not but to wash his feet' (John 13:10), we gather that Peter and Christ's other disciples had been baptized, either with John's Baptism, as some think; or with Christ's, which is more credible. For He did not refuse to administer Baptism, so as to have servants by whom to baptize others."
Reply to Objection 3. Those who heard the preaching of Peter received the effect of Confirmation miraculously: but not the sacrament of Confirmation. Now it has been stated (ad 1) that the effect of Confirmation can be bestowed on man before Baptism, whereas the sacrament cannot. For just as the effect of Confirmation, which is spiritual strength, presupposes the effect of Baptism, which is justification, so the sacrament of Confirmation presupposes the sacrament of Baptism.
Source: Summa Theologica (New Advent)