There is no public transport to Nouamghar. The standard approach is by 4x4 from Nouakchott — about 155 kilometres up the beach at low tide, or on the inland piste track when the sand is too soft. The tide-dependent beach drive takes around four hours; do not attempt it without an experienced local driver who knows the tide tables.
From the north, Nouadhibou is roughly 220 kilometres away across the desert via the Cap Blanc peninsula. Tour operators in both Nouakchott and Nouadhibou run Banc d'Arguin trips that include transport, a park permit, and accommodation in Imragen camps.
You must hold a Banc d'Arguin park permit (purchased in advance in Nouakchott, Nouadhibou, or at park headquarters) to enter the area legally.