Given the current situation i would strongly reccomend you to apply only through referrals!
You may either try to network on your own and secure a referral or use the network of others.
Here I would like to explain you the mechanics how referrals usually work:
My mentee sends me the documents (CV and cover letter) for a specific company.
I have a very wide network of friends, former colleagues and ex-mentees on high positions in consulting (partners, principals and managers) across the world. I chat with them individually praising your competences and skills. Afterwards, I ask them to follow your documents on their behalf directly to their HR ladies while putting a word for you.
In that way you may get your “partner referral” which normally brings you in the pole position for the interview. You may compare it to “skipping the line for business class” at the airport.
If you have any questions, just send me a direct message. – I am happy to answer your questions and help you getting interview invites and convert them to offers.