I have a master's degree in HSE + a master's degree in English/Arabic Translation ... How can I overcome my lack of experience and start my career?

Just start any opportunity in your degrees , and the experience will start flowing. 

one suggestion - get involved as a volunteer with a company that you like to work with.

Start from the bottom just like climbing up a ladder, you cannot become a manager easily unless your father is the owner of the company. Start being an OJT. I suggest select one of the best company first as it will be your stepping stone.

Vow, a person like you is rare in the market given your HI-LEVEL of bilingual ability and your interest in HSE.  I would suggest just get whatever job you can get and get involved as lot of poeple have said.  Unless you dont get your hands dirty, you will not get the experience.  There is no substitution for experience at all.  You need to get involved and work and get experience.  If possible with a senior HSE guy till such time that you see and live HSE even while in bed.  Thats when you are ready to demand higher perks and senior positions.  I was looking for someone like you a few weeks back.  

I would also suggest that whatever you write, write your own.  Write your own manuals. Write your own procedures and policies even.  Make your own forms as per needs arising.  You can research on the net for all this but at the end your product should be 100% customised to your settings.  I have met a lot of people who tried to sell me cut, copy, paste stuff during ISO certifications.  Its disgusting when someone does that when being paid millions.   I would strongly advise to write your own stuff by experience and be seen different from others.  Its very tempting to do what everyone does but if you really want to be a professional then you need to be seen different and Customisation is the key.  Dont be afraid to challenge the status quo.  thats what a leader does.  see if something needs to be changed or revised.  If you do feel that urge some day, the knowledge to change it or write something is already there with you, trust me.  otherwise you will never feel the urge to challenge or change somehting

I go for the suggestion by Mr. Khalid mahmood. I think it will work! 

Practice online activities, approach voluntary work........etc.

Just do one thing Don’t discourage your self always think positively and learn the things which your not able to understand. Be a confident man,  confident = experience