Ask HN: Process for immigration (US / Aus)

I've asked a question previously on whether to apply for a h-1b visa first or a job first (US specifically), and it had no replies.

I'm reading the Australian skills assessment requirements [1] on the Aus Computer Society and I'm not going to be able to get some of these documents for my job history: I quote

"Employment References

Each employment reference must contain: • Start and Finish Dates of Employment • Description of Duties Performed • Hours worked - Full time or Part time • Country where Employment was completed • Company Letterhead and signed by the author

Please Note:  Employment references MUST contain an end date or the work episode will be assessed as not suitable.  Employment references can only be calculated until the date of submission. The “To Date” will be taken from the employment reference date or the submission date of your application – whichever comes first.  If there is no date indicating when the employment reference was written, the reference will be assessed as not suitable.  If your employment reference is “Current”, it MUST be dated and the “To Date” will be noted as the date of the submission of the skills assessment.  Only month and year will be counted for employment duration, not individual days.  The relevance to your nominated occupation will be determined by the description of duties in your work reference.  If dates or duties are unclear or open to misinterpretation, the work episode will be assessed as not suitable. "

Why? because some of the companies i've worked for have literally closed down and I have no means of getting any of these documents as specified.

So can i just apply for jobs at big Co and hope someone will sponsor? or am i in a spot of bother?

[1]http://www.acs.org.au/__data/assets/pdf_file/0020/7319/Skills-Assessment-Guidelines-for-Applicants.pdf