I will assume that your fiancée is still holding legal visiting status in the States. If your fiancée is currently in America just visiting, your alternatives would appear to attempt to adjust her status to permanent residence while she is here or having her return to Japan at which point you can either apply for a K-1 fiancée visa on her behalf or begin the I-130 relative petition process for her green card. If staying here to adjust status, she may have to explain that she did not have that purpose in mind when she entered the US. A K-1 fiancée petition will usually take approximately 6-9 months while an I-130 relative process approximately one year.
Assuming you are a US citizen, she can remain here and you can get married after she has been here for 90 days. She can then adjust status to that of permanent resident using the one-step application process.
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