The most conventional approaches to find axion-like particles (ALP) or notably axions typically lies on their coupling with photons. However, if the coupling is extremely weak then there is a chance that they decouple themselves from the standard model physics and becomes invisible which are a source of stochastic gravitational waves at the epoch of the early universe formation, solving the riddle of the axion origin mystery and the origin of weak gravitational waves. Having the axion decay constant rates as 𝑓≥1016−1+1GeV, the axion signals which can be detected by either ground/space based observatories or pulsar timing arrays shows a broad space parameter of axion mass thus helping to probe the exis-tents of invisible axions originating in the early universe. The ALP or axions generally couple to a dark gauge bosons which at the onset of oscillations produces tachyonic instabilities that increases the visible parameter for the ALP or axion dark matters. The quantum fluctuations that arises and getting amplified by the strong coupling of axion/ALP to dark boson modes sources chiral gravitational waves (GWs). The accurate spectrum of these GWs have been calculated from the U(1) gauge fields pro-duced by axion dark matters. The explosive outbursts of gauge fields indicates the advantage of non-linear data analysis over linear modes to calculate the exact GWs spectrums. The ground/space based interferometers and pulsar timing arrays have the ability to probe the bottom up approach of the axions, in the weakly coupled regime which otherwise remains unconstrained. Further, it has been discussed the kinetic mixing mechanism and the dark gauge photon mass over the insensitivity of the couplings to standard model fields. The ALP scenarios or realistic axions may provide us useful infor-mations about the signal templates of the early universe, as well as useful datas for GW experiments. Throughout the paper we will assume the axion field being homogeneous the equations of motions for the gauge boson modes depend on the parametric valued scales 𝑘 =𝑘.