‘ Therefore we said, “Let us now build us an altar, not for burnt offering, nor for sacrifice, But it shall be a witness between us and you, and between our generations after us, that we might do the service of YHWH before him, with our burnt offerings, and with our sacrifices, and with our peace offerings, that your children may not say to our children in time to come, ‘You have no part in YHWH'.” '
The purpose of the altar is clearly stated. It was not for use but as a witness that they too were the true people of God with rights of inheritance given by YHWH. Thus would they be able to join in the tribal gathering at the central sanctuary for worship and sacrifice without fear of being turned away. This all brings out how deeply they had had burned within them the centrality of the central sanctuary to the covenant and to their part in YHWH. At this time the true faith of YHWH was held with fervour.
“Let us now build us an altar.” Literally ‘Let us now do (what is necessary to prevent this) in building us an altar'.
“Burnt offerings -- sacrifices -- peace offerings”, compare Joshua 22:23. They were well aware of the different types of sacrifices to be offered to YHWH.