Yes, Gravitational waves as originally predicted can always existed.
Unfortunately for those scientists who have tried for over 40 years to detect them, the Theory of General Relativity had an ability via mathematics to postulate their existence, but was unable to provide the required physical details to enable a delineation of them.
The recent detections at LIGO were not true gravitational waves. The detections were the results of large amounts of matter being phase changed into heat, and magnetic pulses in the form of Gamma Rays, that traveled spherically outwards from the source of mass destruction.
The ESA missed a physical advancement when the spacecraft Rosetta provided an example of mass phase conversion while it investigated Comet 67/P. The unexpected heating at long distance from the Sun and the gradual appearance of a increasing magnetic field around the Comet, was a micro example of the event that resulted in the LIGO detection.
Both LIGO and Rosetta detected a Gravitational Thermodynamic Effect (GTE)
To detect rapidly occurring gravity waves, the experiment would need to be made at the microscopic level of physical reality.