The increase came in a week when Mr. Murphy, encouraged by other measures that showed New Jersey making progress in fighting the virus, began to sketch out how the state might reopen in the weeks ahead.

NEW YORK TIMESのコロナ関連の記事です。
1行目のwhen以下は、主語がMr. Murphyで、述語はbegan to sketch outなのかなと思いますが、よく分かりません。