How do Trinitarians understand what it means for Jesus to grow 'in favor' with God?

Cornelius à Lapide, The Great Commentary (vol. 4): S. Luke's Gospel, on Lk. 2:

Ver. 52.—And Jesus increased in wisdom and stature, and in favour with God and man. For stature the Greek has ἡλικίᾳ, “age,” or “proficiency.” See also chap. 12:25. Both renderings are true and apposite.

To the question whether Jesus really progressed in wisdom and grace, as He did in age and stature, S. Athanasius (Serm. 4 Contra Arianos) and S. Cyril (Thesaurus, 1. x.) seem to answer in the affirmative; for they seem to say that the humanity of Christ drew greater wisdom from the Word by degrees, just as the Blessed Virgin and other men and women did.

But the rest of the fathers teach differently. For, from the first instant of His conception, Jesus was, as has been said at v. 40, full of wisdom and grace, this being due to that humanity on account of its hypostatic union with the Word. S. Gregory Nazianzen (Orat. 20 in laudem Basilii) says, “He progressed in wisdom before God and men, not that He received any increase, since He was, from the beginning, absolute in grace and wisdom, but these gradually became apparent to men [hitherto] unaware of them.” For, as Theophylact says, “the shining forth of His wisdom is this very progress;” just as the sun, though it always gives the same degree of light, yet is said to increase in light as it unfolds it more and more from morning until midday. It is to be noted that there were in the soul of Christ three kinds of knowledge—(1) beatific, by which He saw God, and all things in God, and so was rendered blessed; (2) knowledge infused by God; (3) experimental knowledge guided by daily use. The two former were implanted in Christ in so perfect a degree from the first moment of His conception that He could not increase them. I assert the same with respect to His habitual grace and glory. So say S. Augustine (De peccat. mor. et rem., l. iii. c. xxix.), S. Jerome (on the words of Jer. 31:22, “A woman shall compass a man”), S. Athanasius, Cyril, S. Gregory Nazianzen, Bede, and others, S. Thomas and the schoolmen everywhere—for this is required by the hypostatic union.

Christ, therefore, is said to have progressed in wisdom and grace as He progressed in years—1. In the estimation of men, and in outward seeming. For sometimes Scripture speaks according to what is seen outwardly, and the judgment formed by men. So Origen, Theophylact, Nazianzen, S. Athanasius, and Cyril.

2. Christ did really increase in experimental wisdom, for from mere use He acquired experience—“He learned obedience by the things which He suffered” Heb. 5:8.

3. Though Christ did not increase in habitual, yet He did increase in actual and practical wisdom and grace. For, even while yet a child, He daily exerted more and more of the strength of mind and heavenly wisdom that lay hidden in His soul; so that in face and manner, in word and deed, He ever acted with greater and greater modesty, gravity, prudence, sweetness, and piety.

To the objection that Christ is said to have increased in grace before God, S. Thomas (p. iii. Quæst. vii.), answers that Christ increased in grace in Himself, not as regards the habit, but as regards the acts and effects produced by it.

Among other differences between the grace which Christ had, and that which we have, there are the four following:—

1. Christ had grace, as it were, naturally by virtue both of the hypostatic union and of His conception of the Holy Ghost; but with us all grace is undue, gratuitous, adventitious, and supernatural.

2. In us grace (1) wipes out original sin, and whatever actual sins there may be, and so (2) makes us pleasing to God; but in Christ grace existed not only previously to sin, but actually without it, sanctifying Him per Se primo, for from the grace of the union with the Word emanated habitual grace, as rays from the sun, immediately and naturally. So that we are adopted and are called sons of God, but Christ is truly and naturally the Son of God, as S. Hilary (De Trinit., l. xii.), and Cyril (In Joannem, l. iii. c. xii.), teach.

3. In us grace is peculiar to the individual, justifying the man in whom it resides; but the grace of Christ is the grace of the Head, and so sanctifying us. For “of His fulness have we all received, and grace for grace” S. John 1:16.

4. Grace increases in us (even in the case of the Blessed Virgin) by good works; but in Christ it did not increase, because, proceeding from the union with the Word, which from the beginning was full and perfect, this fulness of grace, which could not be increased, was given Him at the moment of that union.

Tropologically, Damascene (De fide, l. iii. c. xxii.) says that Christ progresses in wisdom and grace, not in Himself, but in His members, that is, in Christians. For He went on producing greater acts of virtue day by day that He might teach us to do the same. All our life is without ceasing either a progress or a falling off; when it is not becoming better it is becoming worse, as S. Bernard tells us. Ep. 25.

From a physical perspective, Jesus grew in all these things, even though He was still fully God the entire time. For example, we could say His physical body grew in "stature", even though the heaven of heavens cannot not contain Him (cf. John 3:13, KJV). His physical muscles grew as ours, which is how He could feel our pain and tiredness (John 4:6); and yet, whenever He chose, He could override this and walk on water (Matthew 14:25). He decided to be homely physically (Isaiah 53:2); and yet, whenever He pleased, He could be transfigured gloriously (Matthew 17:2). He allowed His physical brain to develop through natural processes, meaning that His physical brain could grow in "wisdom", even though He was always omniscient all along (John 21:17, Matthew 9:4), and often demonstrated that, knowing things which were impossible with only a physical brain. As He allowed His physical body to grow in these areas, so also would His close relationship with His Father become more manifest ("God" refers specifically to the Father in that verse); and so from our perspective, His favor with God would "grow" or become manifest to others, even though He had it all along (John 17:5).

I've heard someone describe it as a rose; as it blooms, its beauty is hidden inside, and we slowly see more of it. In that sense, it "grows" in beauty, though technically, the beauty is already inside, waiting to be revealed.

According to Philippians 2 we are to have within ourselves the same mind that was in Christ Jesus. So then Jesus had, in himself, the mind that:

Though he was in the form of God He did not cling onto that but instead He emptied himself by taking the form of a servant. (v. 6-7)

Having been found in human form (servant) he humbled himself by obedience all the way to death. (v.8)

So, Jesus' mindset was that he had let go of the morphe (form) of God and took on the morphe of man. He knew this about himself.

Obviously growth would be necessary. He had to grow physically, mentally, etc. from a human fetus. He had to learn language, custom, etc. as a human child.

By the time the verse in question (Luke 2:52) comes along Jesus is 12 years old. He knows enough about who He is, at this point, (Phil 2, again) to say:

Luk 2:49  And he said to them, “Why were you looking for me? Did you not know that I must be in my Father's house?”

Literally he says "the Father of me", which is the same sort of claim for which the Jews wanted to kill him later on:

Joh 5:18  This was why the Jews were seeking all the more to kill him, because not only was he breaking the Sabbath, but he was even calling God his own Father, making himself equal with God.

And he has just been in the temple for three days listening and asking questions which amazed everyone who was there:

Luk 2:46-47  After three days they found him in the temple, sitting among the teachers, listening to them and asking them questions. And all who heard him were amazed at his understanding and his answers. 

So Jesus increased in wisdom (mental) and in stature (physical) as a human being. And also in favor (actually grace) with God and man. He grew in grace by obedience through humility, as we all must. This growth was part of his humility...part of the great condescension of Philippians chapter 2...part of the mystery of Godliness.

He did not grasp at the form of God which He had but He emptied Himself and took on our form. Just as He did not abandon the form of God that He had when he came down (He did not abandon but emptied), so He did not abandon the form of a man when He went back up and lives forever as our mediator, high priest, Lord, and king.