Don’t hesitate to start a sentence with But. It’s a coordinating conjunction, and great writers have been starting sentences with conjunctions for hundreds of years. You can remember the coordinating conjunctions by referring to the acronym BOYFANS: but, or, yet, for, and, nor, so. You can begin a sentence with any of these. And you should.
Here’s Justice Hugo Black:
The Framers knew, better perhaps than we do today, the risks they were taking. They knew that free speech might be the friend of change and revolution. But they also knew that it is always the deadliest enemy of tyranny. Hugo Black, The Bill of Rights, 35 N.Y.U. L. Rev. 865, 880‑81 (1960).
In fact, you should avoid “However,” as a sentence-starter.
Try But instead.
You'll find a thorough discussion of coordinating conjunctions in the Parts of Speech section of Grammar.com. Click here for the beginning of that discussion.