This phase I/IB trial tests the safety, side effects, and best dose of ipatasertib in combination with paclitaxel and carboplatin in treating patients with stage III or IV epithelial ovarian cancer. Ipatasertib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Paclitaxel is in a class of medications called taxanes. It stops tumor cells from growing and dividing and may kill them. Carboplatin is in a class of medications known as platinum-containing compounds. It works in a way similar to the anticancer drug cisplatin, but may be better tolerated than cisplatin. Carboplatin works by killing, stopping or slowing the growth of tumor cells. Giving ipatasertib in combination with paclitaxel and carboplatin may lower the chance of the tumor growing or spreading for longer than the paclitaxel and carboplatin alone.