It is unfortunate that these 'big companies' will not consider candidates who have worked with an establishment that has been blacklisted by EPFO for non-remittance of PF dues when the non-remittance is not related to the fault of the candidate. If you are applying through an offline platform, there should not be any problem. Moreover, if you have the opportunity to discuss your past experience, it should not create any issues because you can explain that it was not your mistake that the company became blacklisted. I believe that if it is true that you cannot even apply for better opportunities if your company is blacklisted, the issue should be escalated, preferably choosing a common/public platform.
In a practical scenario, nobody will delve deep into such matters. If you observe the list of defaulters displayed in the Regional and Sub-Regional Offices of EPFO/ESIC (the list is available on the website itself), you will notice that most of the companies are very reputable, including public sector companies, which had to close down due to financial issues or reasons unrelated to employee unrest. Therefore, why should we, as HR professionals, turn hostile against the employees only?