"Nosco", not "gnosco", was the usual form, because of a pre-Classical sound change of word-initial gn- to n-
As Joonas Ilmavirta♦'s answer indicates, gnosco was an "old form" (Lewis & Short), not the usual form in Classical Latin. Lindsay (1894) says "Initial Latin gn became at the beginning of the second cent. B.C. n (as in Engl. 'gnat'), e.g. nōsco, older gnōsco" (p. 294, §119, The Latin Language: An Historical Account of Latin Sounds, Stems and Flexions).
Words that were spelled with word-initial "gn" in Classical Latin may have been pronounced with either [gn] or [n]; [ŋn] might have been used in Old Latin
Because of that sound change, it was not regular for gn- to appear at the start of a Latin word in the Classical period. Word-initial gn- appears as an apparently archaizing or conservative spelling in a few native words or names, and also in loans from Greek, where γν- had remained intact in word-initial position.
The pronunciation isn't clear. As far as I know, there's no explicit evidence for Latin gn being pronounced as [ŋn]. That pronunciation is thought to have been used word-internally because of certain indirect evidence. (As I mention in my answer to "How do we know how gn was pronounced in Classical Latin?", there is some uncertainty about whether gn might have been pronounced as [gn] even in word-internal position.) It doesn't seem impossible to me that word-initial [ŋn] existed at some point either in Old Latin (as a step in the historical sound change from gn- to [n]) or in Classical Latin (as an allophonic realization of gn in this position, as in word-internal position), but I don't know how we could ever know.
Allen (1978)'s section on gn indicates that the name Gnaeus was probably pronounced with either [gn] or [n]:
in initial position Terentianus Maurus seems to suggest the normal [g] value in the name Gnaeus when, referring to the spelling of the name with Cn., he says
g tamen sonabit illic quando Gnaeum enuntio
(K. vi, 351).
But in fact by this time any pronunciation of the initial G must have been artificial; as Varro already observes (fr. 330 Funaioli), ‘qui G littera in hoc praenomine utuntur, antiquitatem sequi uidentur’. Varro also notes a spelling Naeum (and Ναιος is common in Greek).
(p. 24, Vox Latina, second edition)
Old Latin apparently didn't have any words with initial [kn] (clusters like *kn in inherited vocabulary seem to have developed to <gn>, merging with etymological *gn). Because of this, there is an argument based on typological
grounds that in Old Latin, words spelled with initial <gn> were pronounced with [ŋn] instead of [gn] (Ranjan Sen, 2015, Syllable and Segment in Latin, p. 183). But even if that argument is valid, it doesn't say much about the usage in Classical Latin, since Allen indicates that any pronunciation other than [n] would have to be regarded as "artificial" in that time period.
Light scansion of a preceding vowel is probably not sufficient evidence to conclude that a word was pronounced with [n]
A preceding short vowel would most likely have scanned as light before either [n] or [gn], so metrical evidence of light syllables being used before (g)nosco is probably not relevant. The scansion of Latin consonant clusters is problematic because of apparent influence in this area from Greek. Here is a passage with relevant information from Seppo Heikkinen's "The Christianisation of Latin Metre: A Study of Bede’s De arte metrica" (apologies for the huge block quote; I didn't have time to figure out how to communicate the important bits in a shorter way):
word-initial “mutes with liquids” hardly ever lengthen the final syllable of the previous word in Latin poetry. The few exceptions to this rule in the classics are probably due to the emulation of Greek models40 [...] this is one of the examples of pre-Christian prosodic “negligence” that came under Bede’s attack in his chapter on the prosodic differences between pagan and Christian poets.41
Especially in Greek metre, the nasals m and n are usually classified together with the liquids proper, because [...] the combination of plosive and nasal either may or may not create a position after a short vowel. In Greek verse, the rules, as in the case of proper liquids, are considerably more flexible than in Latin, but usually a word-initial combination of plosive and nasal (as in tmesis, pneuma etc.) does not create a position after a short vowel.42 In Latin verse, the rules governing Greek loans with plosives with nasals are essentially the same as those governing plosives with liquids. The only “native” consonant-nasal compound of any relevance in this context is gn, which creates a position word-internally but never word-initially; in reality, the g may have, already in classical Latin, been pronounced as a velar nasal (as in English hangnail), except at the beginning of a word, where it was possibly silent.43
Bede discusses both word-internal and word-initial gn at the end of his chapter on common syllables. He mentions the compound in conjunction with the letter x, their common feature being the fact that they only create a position word-internally but not word-initially. Bede accepts the classification of n as a liquid,44 because initial gn is analogous to initial plosive and liquid, but emphasises that, unlike plosives with “other” liquids, it does not make a true common syllable. Bede implies that this observation is his own, and demonstrates this with an appropriately uplifting quotation from Prosper:
N quoque littera pari ratione, ni fallor, cum in medio verbo consonanti alteri fuerit subiecta, praecedentem syllabam sive natura seu positione semper longam habet, ut ‘regna’, ‘calumnia’. Cum vero in primordio verbi fuerit alii subiecta consonanti, ut ‘Gneus’, ‘gnarus’, profecto ultimam syllabam verbi prioris, si in brevem desierit vocalem, brevem hanc, ut fuerat, remanere permittit, neque ullam producendi habet potestatem, Prospero teste, qui ait:
Nec tamen hos toto depellit foedere gnarus,
naturam errantum dividere a vitiis (Prosp. epigr. 67, 3-4).45
40Raven 1965, 25; e.g. “lappaequē tribolique” (Verg. georg. 1, 153); “per impotentiā freta” (Catull. 4, 18).
41 DAM 16; Orchard 1994, 75-76. [...]
42 Raven 19682, 23.
43 Allen 19782, 23-25 [...]
44 In accordance with traditional terminology, Bede classifies nasals as liquids already in his chapter on the letter (De littera), see DAM 1, 56-60.
45DAM 3, 127-136.