For a general sense of progression:
* E hele ana mākou i mua. (eh-leh-ah-nah mah-kow ee moo-ah) - Literally "We are going forward."
* Ke neʻe nei mākou i mua. (keh-neh-eh nay mah-kow ee moo-ah) - Literally "We are moving forward."
For a more specific sense of progress or advancement:
* Ke holomua nei mākou. (keh-ho-lo-moo-ah nay mah-kow) - This means "We are progressing" or "We are making progress."
* E hoʻomau kākou i ka holo. (eh ho-oh-mah-oo kah-koo ee kah ho-lo) - This means "Let us continue to move forward" or "Let us keep going."
For a more metaphorical sense of moving on or leaving the past behind:
* E haʻalele kākou i ka wā i hala. (eh ha-ah-leh-leh kah-koo ee kah vah ee ha-lah) - This means "Let us leave the past behind."
* E nānā i ka wā e hiki mai ana. (eh nah-nah ee kah vah eh hee-kee may ah-nah) - This means "Let us look to the future."
The best choice for you will depend on the specific context and the nuance you want to express.