What data specifically are you claiming refutes the Big Bang?
The redshift anomalies have always refuted the Big Bang.
The lack of pop 3 stars.
The inability to predict the smoothness of the background radiation.
The fact that there have not been enough supernova remnants
The presence of long period comets in out solar system.
The faint young sun paradox.
High speed stars within globular star clusters.
The presence of spiral galaxies.
And the Webb telescope is finding more all the time,
That is why many are proposing many alternatives to the Big Bang.