Is it permissible to marry a Muslim girl عرفيًا (customarily/secretly), while concealing one's Islam and not publicizing the marriage, for fear of family, and to facilitate meeting and avoid prohibitions, with the intention of formalizing the marriage later?

There is no harm in concealing one's faith for fear of harm. Marriage is valid if its pillars and conditions for validity are met, even if it is not publicly declared or officially registered.

So, if the girl is proposed for from her guardian, and he marries you in the presence of two just witnesses and with the contract documented, there is no harm. However, if it is without her guardian's knowledge, it is not permissible, as his permission is necessary.

Your relationship with the girl must adhere to the Shariah limits; no meetings, no private seclusion (khalwa), and no forbidden acts.