This response assumes you are in England ...
There is no downside for you to ask to view it, provided you expect you can finance the amount you'd offer for the house, between your deposit and the mortgage amount you'd expect to be able to borrow!
Were I in your circumstances, I would ask for a viewing and tell the estate agent that I was moving to the area for a new job. If they started to ask questions about my ability to buy the house, I would answer truthfully, and from a place of confidence that I was a legitimate buyer, but I would not start to answer questions that were not being asked. If they asked me whether a mortgage offer was already in place, I would tell them that I already have a mortgage advisor who had told me I could afford the house [assuming this was true!] but that specific mortgage offers will depend on the specific house. I would ask the advisor ASAP how much I could expect to borrow on the new salary, taking into account that it is new. I would also make your offer more serious by appointing solicitors to represent me in my purchase; that can be done before choosing a particular house on which to make an offer.
In England, anybody can put in an offer on any house any time they want, without any specific requirements. It does not become legally binding until you exchange contracts. It's just important not to make frivolous offers and then walk away like a flake because that can leave you blacklisted with estate agents. But in your circumstances, I don't believe an offer backed up by advice from a legit mortgage advisor would be even close to frivolous!
If you can find a good mortgage advisor who is confident that you will be able to borrow enough on your new salary to afford the house, and especially if you have already exchanged contracts on your own house, then you are not in that weak of a position. In that case You can truthfully tell the estate agent all of the following:
a) contracts have already been exchanged on the sale of your current home, with completion on date X, at which point you will move into rental accommodation in order to be a chain-free buyer. The deposit you expect to have available will be £Y (this assumes you can already work out the size of deposit you will be able to put down; this is especially worth mentioning if equity in your current home will leave you with a relatively large deposit. Do remember to factor in funds for SDLT, nd solicitors' fees, + other transaction costs such as the building survey)
b) you are highly motivated to buy in this area because you are moving to the area for a new job, which is also at a higher salary;
c) You are working with a mortgage advisor to help you find the best terms available for this purchase. They have promised a recommendation for you by date Z [hopefully the mortgage advisor can give you a good idea how long after June 1 it will take to get mortgage offers in, and will be able to put all the required paperwork together ahead of that date].
Obviously a cash buyer would still be in a stronger position than you, but as a highly motivated buyer who had already sold their home and needed to move to the area, your offer should also be pretty credible.
Were I the seller I would of course realise that a person moving for a new job won't be able to complete if the job falls through, but I would definitely want you to view my home!