Yes, using 'regardless' in the beginning of a sentence is perfectly acceptable, and infact, is used extensively by many people.
To understand the usage of the word 'regardless', try going through these examples. Notice how almost all sentences that use the word 'regardless' is followed by the preposition 'of'.
One can roughly translate "Regardless of" as 'Even though'.
It is generally seen that 'regardless' is usually succeeded by an 'of' when used in a sentence. There may be sentences that omits the preposition after 'regardless', none of which are in my head though. So, one can say that this is a general rule, but yes, there can/ may be exceptions.
It is a general usage to say "Regardless of something".
Try going through this post and this one also.