Well, one of the major obstacles to overcome is getting to the 5th heart as Naryoril mentioned. There really isn’t anyway to increase it other than using the idol or using up (or eating) those chocolates the idols give to you on Valentine’s Day.
Meaning, you’ll have to do lots and lots and lots of grinding, and unfortunately there really isn’t any way around it. Once you get to the 5th heart, things become a little bit easier since all the grinding helps with everything like getting more money, memories/bursts lvl (also assuming you’re also doing Lv3 lessons), song level, etc. And, you’ll be able to complete those early DL lives to help obtain more S-rank costumes.
Of course, your next obstacle then is to get to S rank which is 10 million fans. Though, I would recommend getting at least 2 idols to S-rank because that way you’ll automatically have enough total fans to unlock all the songs in the game. Fortunately, to those that are playing the game later or haven’t gotten far, there are one time DL lives which give like a million fans per live. (Those didn’t exist when I played the game, so I had to do that paid promotion a huge number of times which is very expensive.)
There’s also DLC money and recently DLC stat boosting item to help speeds things up too.
And, as Naryoril mentioned, there are some strategies to help you score higher, so it's worth checking out your accessories/costume making sure you have the optimal combination. Personally, I never have to use Master version of songs except during difficult DL lives since I don’t have the costume requirements.