I am not eligible for Chapter 7 yet so I will file Chapter 13 and then convert when I am eligible for Chapter 7 discharge.

Unfortunately no. Discharge eligibility is determined at the time a bankruptcy case is filed. At the time of the case is filed, using the date that the case was filed, it is determined whether the debtor or debtors is/are eligible to receive a bankruptcy discharge. Given that there are different time limits depending first on which chapter of bankruptcy you filed previously and depending second on which chapter of bankruptcy you are filing under now, a debtor may be eligible for discharge under one chapter of bankruptcy and not eligible for discharge under another chapter of bankruptcy. The most common reason that a debtor is not eligible for discharge is due to a previous discharge. This can almost always be overcome by the debtor waiting to file until the time limit has passed based on the chapter of bankruptcy they filed previously and the chapter of bankruptcy they are filing under now. The guidelines are as follows:

If you filed a prior Chapter 7 and now want to file a Chapter 7, you must wait 8 years to file from the filing date of the first petition.

If you filed a prior Chapter 13 and now want to file a Chapter 7, you must wait 6 years to file from the filing date of the first petition.

If you filed a prior Chapter 7 and now want to file a Chapter 13, you must wait 4 years to file from the filing date of the first petition.

If you filed a prior Chapter 13 and now want to file a Chapter 13, you must wait 2 years to file from the filing date of the first petition.

So, you need to file again but have not reached the time limit to receive a discharge. Yes, you can still file a Chapter 13. You can be in a Chapter 13 bankruptcy without receiving a discharge. However, you cannot simply convert to a Chapter 7 when the time limit has passed because again, eligibility was determined on the day the case was filed. You are not out of luck. You can dismiss the Chapter and file a new separate Chapter 7. Because this is a whole new bankruptcy eligibility for discharge is then determined by the new filing date.