Context: I have Bachelors and Masters in Industrial Engineering. I graduated and did IE at Fortune 100 company for about 2.5 years and am now Manager in organization for engineering for over 1 year.

1. Without direct management experience (leading people, professionals) most companies wont risk hiring you as a Manager.
2. However, your experience could put you in position to manage operations or teams, but more at a 'supervisor' level. I have a friend working at Amazon, IE degree, manages a 'production' team in distro center (supervisor). This type of role could be a good fit. fyi: In most corporate or larger organizations: Director > Manager > IE/Analyst/Supervisor > Ops/Production.
3. Look at positions labeled as IE or Analyst.
4. I have hired people from small companies. i dont care. what i look for is experience, skills, competencies, and results. focus on showing what you accomplished, skills used, and results achieved.
5. you can probably do inventory planner job. review job posting, pay attention to duties, resposibilities, etc. can you do those? if i was wanting an inventory planner, id prob be looking at: can work w data, can assess data, can form decisions or recommendations (orders), ability to forecast demand, robust framework for assessing planning horizon, could you do it ad hoc in excel if asked, are you familiar with any specific software we use to do it, are you familiar with inventory planning and modeling concepts or approaches (holding costs, shortage costs, lead times, capacity constraints, reorder points, optimal ordering quantities), etc.
6. stop focusing on 'small company'. dont utter it in interview or resume. focus on your experience and skills.
7. big companies like results. and like quantified results. consider how you can demonstrate: saving company money with improvements (how much), keeping inventory in stock, minimizing shortages, minimizing holding costs, etc. #s, #s, $s, and $s.
8. i wouldnt worry about certificates. i feel it is a money and time waste. i dont pay attention to them in hiring decisions. however, if you want to move more into supply chain or logistics world, see if they have any mandated certs by law or such.
9. as employer, i will look at your work experience since you have been out of school more than a year. i wont pay attention to school much. focus on this. (other than making sure you have an equivalent degree)
10. on that pt, remove your GPA and dont share unless asked. large employer wont care much at this point. that said, when i recruit at university with students, i do automatically exclude GPA <3.0 from consideration, on baseline many tend to exhibit higher tendencies to be lazy, unmotivated, less intelligence/problem solving skills, difficulty priorotizing, etc. (for engineers)
11. update your resume to reflect you are working, and not in school. work history up top, education degree toward bottom, etc.
12. working in supply chain, logistics, inventory, etc is one pathway for IEs. But consider other similar roles IEs do, even with diff work or industries: analysts, project managers, projct analyst, business analyst, manufacturing indutry, servicing/consulting industry, healthcare industry, six sigma, lean process improver, process improvement engineer, systems engineer (not computers), etc.
13. reflect the job on your resume as 'ABC Corp' or whatever. dont mention or share it is your parents company, in resume or interview. position it as a job doing as you describd for warehouse of small 30 person company, etc. this keeps focus on you and your work. if yu told me it was your parent company, it would raise red flags: did u only get this job because of that, are you unqualified, are you inflating your duties, why were u then unable to find other employment post university, etc.

good luck