Proteins are by definition polypeptides, linear chains of aminoacids linked by amide bonds. There are various layers of information that allow one to conclude that a sample consists of protein. Atomic composition (molecular formula) is not unequivocal evidence (consider the melamine scandal in China) but is a useful constraint. Chemical reactivity is stronger evidence but spectroscopic information is now routinely used.
Any compound with an amide proton (ie a primary or secondary amide group) will result in a crosspeak in the amide region of a $\ce{^1H-^{15}N}$ HSQC NMR spectrum, so such peaks alone are insufficient evidence of connectivity between aminoacids (the chemical shifts and multiplicity do narrow the structural options however). There is however a large family of related higher-dimensional NMR experiments that allow peptide backbone connectivity through the amide bonds between neighboring aminoacids to be determined, as well documented in the literature (2[1]).
Even simplerAlso NOE experiments that establish distance constraints between an amide proton and its neighbors or between nuclei on separate aminoacids can be useful in that regard. Because such experiments can also provide([2]) by providing 3-D structural information theythat can often be regarded as unambiguous evidence of the presence of a peptide bond.
Reference
2: [1] Editor(s): John Cavanagh, Wayne J. Fairbrother, Arthur G. Palmer, Mark Rance, Nicholas J. Skelton, Protein NMR Spectroscopy (Second Edition), Academic Press, 2007, ISBN 9780121644918, https://doi.org/10.1016/B978-012164491-8/50016-6.
[2] Wüthrich K, Billeter M, Braun W. Polypeptide secondary structure determination by nuclear magnetic resonance observation of short proton-proton distances. J Mol Biol. 1984 Dec 15;180(3):715-40. doi: 10.1016/0022-2836(84)90034-2. PMID: 6084719.