As stated above (5; 1, 8), the object of faith includes, properly and directly, that thing through which man obtains beatitude. Now the mystery of Christ's Incarnation and Passion is the way by which men obtain beatitude; for it is written (Acts 4:12): "There is no other name under heaven given to men, whereby we must be saved." Therefore belief of some kind in the mystery of Christ's Incarnation was necessary at all times and for all persons, but this belief differed according to differences of times and persons. [ST II-II, Q2, A7; emphasis added]
So we see that belief "of some kind" is always necessary - but this must be qualified by when and who. With regard to man before the Fall:
[B]efore the state of sin, man believed, explicitly in Christ's Incarnation, in so far as it was intended for the consummation of glory, but not as it was intended to deliver man from sin by the Passion and Resurrection, since man had no foreknowledge of his future sin. He does, however, seem to have had foreknowledge of the Incarnation of Christ, from the fact that he said (Genesis 2:24): "Wherefore a man shall leave father and mother, and shall cleave to his wife," of which the Apostle says (Ephesians 5:32) that "this is a great sacrament . . . in Christ and the Church," and it is incredible that the first man was ignorant about this sacrament. [ST, op. cit.]
And with regard to man after the Fall, but before the Incarnation:
But after sin, man believed explicitly in Christ, not only as to the Incarnation, but also as to the Passion and Resurrection, whereby the human race is delivered from sin and death: for they would not, else, have foreshadowed Christ's Passion by certain sacrifices both before and after the Law, the meaning of which sacrifices was known by the learned explicitly, while the simple folk, under the veil of those sacrifices, believed them to be ordained by God in reference to Christ's coming, and thus their knowledge was covered with a veil, so to speak. [ibid.]
Now one thing that we ought to recognize here is that what St. Thomas seems to describe as an explicit belief in Christ here is not at all what we would think of in that way! For he acknowledges that this belief centered upon the sacrifices which foreshadowed the coming Messiah, and even that "their knowledge was covered with a veil." We see also the the distinction between what is required of the learned and what is required of the uneducated, something we looked at earlier.
These things, while important, are of more historical interest in comparison to the last division Aquinas has in mind – namely, the condition of those who have lived since Christ came.
After grace had been revealed, both learned and simple folk are bound to explicit faith in the mysteries of Christ, chiefly as regards those which are observed throughout the Church, and publicly proclaimed, such as the articles which refer to the Incarnation, of which we have spoken above (Question 1, Article 8). As to other minute points in reference to the articles of the Incarnation, men have been bound to believe them more or less explicitly according to each one's state and office. [ST II-II, Q2, A7 again; emphasis added]
Okay, so St. Thomas tells us that we are bound to explicitly believe in "the mysteries of Christ," and primarily those contained in the Creed. But that is not the last word, and it's probably a good thing, because apart from professional theologians I suspect that there aren't many folks who are competent to explicitly believe everything the Church teaches concerning the Incarnation and the Holy Trinity!
The third objection to II-II Q2 A7 asserts that there are non-Christians who "obtained salvation through the ministry of the angels, as Dionysius states (Coel. Hier. ix). Now it would seem that the gentiles had neither explicit nor implicit faith in Christ, since they received no revelation. Therefore it seems that it was not necessary for the salvation of all to believe explicitly in the mystery of Christ." St. Thomas replies (ad 3) first by offering examples of Gentiles who did receive revelations of Christ from God (including Job, 19:25). Even this is not the end, however:
If, however, some were saved without receiving any revelation, they were not saved without faith in a Mediator, for, though they did not believe in Him explicitly, they did, nevertheless, have implicit faith through believing in Divine providence, since they believed that God would deliver mankind in whatever way was pleasing to Him, and according to the revelation of the Spirit to those who knew the truth, as stated in Job 35:11: "Who teacheth us more than the beasts of the earth." [ST, op. cit.]
Hence we see that Aquinas allows even for implicit faith – under the proper circumstances and conditions – in those things that we must "explicitly" believe. This is consistent, for example, with Romans 2:14-15: "For when the Gentiles, who have not the law, do by nature those things that are of the law; these, having not the law, are a law to themselves. Who show the work of the law written in their hearts, their conscience bearing witness to them: and their thoughts between themselves accusing or also defending one another."
Once again, however, we dare not try to play games with God. We have brains, and he would have us use them. We ought not to ignore our duty to understand the truth as best we can, pretending that because it's difficult, or because we aren't able to understand it very well, we are free to leave such things to the experts. No. We must do our best. But God is merciful, and because we are saved by grace, and not by means of nor by virtue of anything that we believe, our weaknesses do not leave us condemned. Only we must not think that the weakness of the theologically flabby man who never lifts a two-pound doctrinal weight is the same as the weakness of those who through no fault of their own are not able to believe these things explicitly.