This seems to be one where the translations, lexicons, and commentaries are in broad agreement: it's meant temporally.
The syntax of the verse
εἰς τὸ εἶναι ἡμᾶς εἰς ἔπαινον δόξης αὐτοῦ τοὺς προηλπικότας ἐν τῷ Χριστῷ.
so that we who were the first to hope in Christ might be to the praise of his glory. (ESV)
In this rendering, τοὺς προηλπικότας is understood to be in apposition to ἡμᾶς;1 an alternative is to make it predicative:2
That we, to the praise of his glory, should be those who have before had hopes in Christ.
Either way, τοὺς προηλπικότας is a substantive participle meant to provide further information about ἡμᾶς (we).
The meaning of προηλπικότας
The word is a hapax legomenon within the New Testament, derived from a prepositional prefix προ- (before) and ελπίζω (to hope). Although prepositional prefixes tacked onto Greek verbs are notorious for creating an unpredictable semantic relationship with the root, προ- usually has a temporal connotation.3 From BDAG, προελπίζω:
to be prior in hoping, hope before, be the first to hope
The lexicon comments on Eph 1:12 (abbreviation expanded, link added):
in such case προελπίζω is to be understood syntagmatically: hope is prior to realization
The lexicon also helpfully mentions Romans 11:35 as an example where it is contextually obvious that there is a temporal contrast drawn by the verb prefixed wtih προ- and a later verb:
ἢ τίς προέδωκεν αὐτῷ,
καὶ ἀνταποδοθήσεται αὐτῷ;
Or who has given [προέδωκεν] a gift to him
that he might be repaid?
The giving must be prior to the repayment.5
In Eph 1:12, there is also a fairly clear indication of the temporal relationship provided in the following verse.
Εν ᾧ καὶ ὑμεῖς....ἐσφραγίσθητε τῷ πνεύματι
In whom you also....were sealed with the spirit
Here, the distinction is drawn between τοὺς προηλπικότας in v. 12 and ὑμεῖς in v. 13. Many (see all three comementaries cited below) have understood 'we' in v. 12 to refer to Jewish Christians as distinguished from 'you,' the Gentile Christians in v. 13. From the Pillar Commentary:4
The prefix προ- can stress the notion of ‘ahead of time’ or ‘beforehand’, and thus the compound verb refers either to those who hoped before Christ’s coming or, as we have taken it, to Jewish believers, the firstfruits of God’s people in the age inaugurated by Christ’s death and resurrection.
1. S.D.F. Salmond. The Expositor's Greek Testament (1897), vol. 3, p. 264.
2. T.K. Abbott, A Critical and Exegetical Commentary on the Epistles to the Ephesians and to the Colossians (New York: C. Schribner's sons, 1909), p. 20.
3. A.T. Robertson, A Grammar of the Greek New Testament in the Light of Historical Research (3rd edition; London: Hodder and Stoughton, 1919), 562-3 [2nd edition, pp. 620-1].
4. P.T. O’Brien, The Letter to the Ephesians (PNTC; Grand Rapids: Eerdmans, 1999), p. 152.
5. This is a much better example in Greek because both are derived from δίδωμι: “has-before-given....after-be-given-back-to”. Or something.