I agree with Nardog that syllabicity is a phonological concept. It is related to phonetic characteristics of an utterance, but not directly equivalent to them. A comparison might be stress: stress is realized in different ways (in different languages, and sometimes even within a single language), and speakers of one language won't necessarily perceive stress in the same position when listening to utterances in another language.
Therefore, I wouldn't attach much importance to the fact that the nasal sounds syllabic to you or to other non-native speakers. For comparison, Spanish speakers commonly hear an extra syllable at the start of English words starting with /sp/, /st/, /sk/ (e.g. spa, scooter), and Japanese speakers hear an extra syllable at the start of English words starting with /kɹ/ (e.g. crown), but that doesn't imply that the usual English pronunciations of spa and crown should be described as or transcribed as having any more than a single syllable.
Phonological criteria: some examples of possible approaches
Rather, I would say it is correct to characterize the nasal portions of prenasalized consonants as syllabic if they behave as syllabic in the prosody of the language. You could determine this by asking native speakers for their intuitions, examining some other part of the prosodic system of the language that you think is related to syllables (e.g. stress placement, minimal word criteria), or examining usage in poetry. None of those methods is failproof, but any of them would provide a more solid basis than the evidence of your ears.
Phonological theories can get complicated
Unfortunately, saying that syllabicity is phonological doesn't mean much, since there are many different theories of phonology. Some issues might be whether "syllabic" refers to a particular "level" of representation, and whether it is possible for a prenasalized consonant to be non-syllabic at one level but to contain a syllabic nasal component at a more "underlying" level.
For example, this paper says that the Bantu language Babole has [i.mbé.sé] as a realization of underlying /N-bésé/, with an underlyingly syllabic nasal phoneme that shifts the syllabicity onto the preceding epenthetic vowel [i] and then fuses with the following voiced plosive to form the non-syllabic prenasalized onset consonant [mb] ("Phonological Asymmetries of Bantu Nasal Prefixes," by Jonathan Choti, page 39). That example isn't directly relevant to your question, as the resulting prenasalized consonant is not word-initial, but I'm including it as an example of how languages can be analyzed as assigning syllabicity to different segments on an "underlying" vs. "surface" level.
Phonetic criteria: I'm not sure
There might be phonetic criteria that you can use to support an analysis of syllabicity vs. non-syllabicity, but I'm not sure what they would be. Duration is the simplest thing that comes to my mind: all else equal, I would expect a syllabic nasal to have a greater duration greater than a non-syllabic nasal.
The article "Morphological function, syllabic and phonetic form
of nasal+plosive combinations in the Bantu language Mpiemo", by
Christina Thornell and Mechtild Tronnier, has a section "Phonetic correlates" that says
experience from studies on Japanese and Yoruba shows that a nasal should have a duration of at least 50ms to be perceived as syllabic (Nagano-Madsen, personal communication).
I haven't tried to measure the duration of the nasal phones in the audio that you linked to.