Synonyms of optimistically

2 Syllables
buoyantly
3 Syllables
cheerfully, jovially, mirthfully, playfully, happily, blithely, gleefully, smilingly
4 Syllables
favorably, hopefully, exultantly, elatedly, hilariously, lightheartedly, sportively, vivaciously
5 Syllables
encouragingly
6 Syllables
exhilaratingly