Most likely, yes. It is extremely unlikely that your employer was unaware of any asbestos exposure. The dangers of asbestos exposure have been well-documented in the industry for many decades, and most employers that worked significantly with asbestos knew of these dangers. It is far more possible that your employer turned a blind eye towards any exposure to try and limit its liability.
Furthermore, your employer is responsible to you for exposures to dangerous substances in the workplace, whether the employer knew of the exposure or not. The reason being is that when you go to work for an employer, that employer has a duty to provide you with a reasonably safe workplace. If your employer fails to provide a reasonably safe workplace with respect to asbestos exposure, either by making sure that you are not exposed to asbestos or by providing you with proven, effective safety equipment, your employer is liable to you for injuries you receive, including chronic, long-term injuries related to asbestos exposure.
The avenue of recovery that you have against your employer is through filing a workers compensation claim. This is a somewhat streamlined process that exists to get money to you faster when an employer’s actions or inactions have physically harmed you. You may also be able to bring separate, civil lawsuits against the manufacturers or suppliers of the asbestos and/or the manufacturers of any safety equipment that you were issued. An attorney experienced in handling asbestos cases can help you determine all possible liable parties and how to structure your case.