Your footnote reads, "Some might expect a preposition or the dative, but see BDAG πιστεύω 2.a.α." According to what Gryllus has kindly provided, the heading 2.a.α. illustrates the use of the dative as the object of πιστεύω (which is exactly what I have said). BDAG goes on to say (according to your footnote) that "οὗ οὐκ ἤκουσαν = τούτῳ." This suggests that the phrase "οὗ οὐκ ἤκουσαν" can stand in for the dative, but this phrase does not occur in John 20:28. The BDAG entry does not support your assertion about the translation of John 20:28.
That part is superseded by Moulton in the current online version:
Some might expect a preposition or the dative, but see BDAG πιστεύω 2.a.α - Ro 10:14b (οὗ οὐκ ἤκουσαν = τούτῳ [about equivalent toεἰς τοῦτον; cp. vs. 14a] οὗ οὐκ ἤκ .); - Blass Debrunner Funk Greek Grammar (BDF, 1961), section 46 (4) Assimilation of the nom. sing. to other cases - Gives 1 Th 5:3 as an example where the nominative is assimilated to another case. But above all, see Moulton: “We have still to gather some noteworthy points in the use of the cases, particularly the Nominative, on which nothing has been said hitherto. The case has a certain tendency to be residuary legatee of case-relations not obviously appropriated by other cases. We have its use as the name case, unaltered by the construction of the sentence in Rev 9:11: the fact that this has classical parallels (See Blass 85) is perhaps only accidental, for we have already seen that ungrammatical nominatives are prevalent in Rev (see p 9), and the general NT usage is certainly assimilation (Mt 1:21, Mk 3:16, Ac 27:1)." (Moulton J. , 1908)