There are ready-made booster chargers available on AliExpress, based on the CN3303. You can use one of those to boost 5 V to the battery voltage.
A BMS is necsessarynecessary, keeping cells in balance and disconnecting if anything goes wrong isn't chargersa charger's job.
This way is more efficient than boosting to 18 V and then dropping the voltage down as those boards boost only to the battery voltage (like 14.8 V when half way charged, up to 16.8 V when fully charged)